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question_answer1)
A body starts from rest and travels 's' m in 2nd second, then acceleration is
A)
\[(2s)\text{ }m/{{s}^{2}}\] done
clear
B)
\[(3s)\text{ }m/{{s}^{2}}\] done
clear
C)
\[\left( \frac{2}{3}s \right)m/{{s}^{2}}\] done
clear
D)
\[\left( \frac{3}{2}s \right)m/{{s}^{2}}\] done
clear
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question_answer2)
The velocity-time graph of a body is shown in fig. The ratio of average acceleration during the intervals OA and AB is
A)
1 done
clear
B)
\[\frac{1}{2}\] done
clear
C)
\[\frac{1}{3}\] done
clear
D)
3 done
clear
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question_answer3)
A bullet fired into a wooden block loses half of its velocity after penetrating 40 cm. It comes to rest after penetrating a further distance of
A)
\[\frac{22}{3}\,cm\] done
clear
B)
\[\frac{40}{3}\,cm\] done
clear
C)
\[\frac{20}{3}\,cm\] done
clear
D)
\[\frac{22}{5}\,cm\] done
clear
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question_answer4)
A body covers 26, 28, 30, 32 meters in 10th, 11th, 12th and 13th seconds respectively The body
A)
from rest and moves with uniform velocity done
clear
B)
from rest and moves with uniform acceleration done
clear
C)
with an initial velocity and moves with uniform acceleration done
clear
D)
with an initial velocity and moves with uniform velocity done
clear
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question_answer5)
The displacement x of a particle at the instant when its velocity is v is given by \[v\text{ }=\text{ }\sqrt{3x+16}.\] Its acceleration and initial velocity are
A)
1.5 units, 4 units done
clear
B)
3 units, 4 units done
clear
C)
16 units, 1.6 units done
clear
D)
16 units, 3 units done
clear
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question_answer6)
The distance time graph of a particle at time makes angles \[45{}^\circ \] with the time axis. After one second, it makes angle \[60{}^\circ \] with the time axis. |
What is the acceleration of the particle? |
A)
\[\sqrt{3}-1\] done
clear
B)
\[\sqrt{3}+1\] done
clear
C)
\[\sqrt{3}\] done
clear
D)
1 done
clear
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question_answer7)
A particle experiences constant acceleration for 20 seconds after starting from rest. If it travels a distance \[{{s}_{1}}\] in the first 10 seconds and distance \[{{s}_{2}}\] in the next 10 seconds, then
A)
\[{{s}_{2}}={{s}_{1}}\] done
clear
B)
\[{{s}_{2}}=2{{s}_{1}}\] done
clear
C)
\[{{s}_{2}}=3{{s}_{1}}\] done
clear
D)
\[{{s}_{2}}=4{{s}_{1}}\] done
clear
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question_answer8)
In 1.0 s, a particle goes from point A to point B, moving in a semicircle of radius 1.0 m (see Figure). The magnitude of the average velocity is
A)
\[3.14\,\,m/s\] done
clear
B)
\[2.0\,\,m/s\] done
clear
C)
\[1.0\text{ }m/s\] done
clear
D)
Zero done
clear
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question_answer9)
If distance covered by a particle is zero, what can you say about its displacement?
A)
It may or may not be zero done
clear
B)
It cannot be zero done
clear
C)
It is negative done
clear
D)
It must be zero done
clear
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question_answer10)
A man of height h walks in a straight path towards a lamp post of height H with velocity v. Then velocity of the edge of the shadow on the ground will be
A)
\[\frac{hv}{H+h}\] done
clear
B)
\[\frac{Hv}{H-h}\] done
clear
C)
\[\frac{H+h}{Hv}\] done
clear
D)
\[\frac{\left( H-h \right)}{Hh}\] done
clear
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question_answer11)
The displacement-time graphs of two particles A and B are straight lines making angles of \[30{}^\circ \] and \[60{}^\circ \] respectively with the time axis. If the velocity of A is \[{{v}_{A}}\] and that of B is \[{{v}_{B}}\], the value of \[{{v}_{A}}/{{v}_{B}}\] is
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{1}{\sqrt{3}}\] done
clear
C)
\[\sqrt{3}\] done
clear
D)
\[\frac{1}{3}\] done
clear
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question_answer12)
An athlete completes one round of a circular track of radius R in 40 sec. What will be his displacement at the end of 3 min. 20 sec?
A)
\[Zero\] done
clear
B)
\[2R\] done
clear
C)
\[2\,\pi \,R\] done
clear
D)
\[7\,\pi \,R\] done
clear
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question_answer13)
A body moves in straight line with velocity \[{{v}_{1}}\], for 1/3rd time and for remaining time with \[{{v}_{2}}\] find average velocity.
A)
\[\frac{{{v}_{1}}}{3}+\frac{2{{v}_{2}}}{3}\] done
clear
B)
\[\frac{{{v}_{1}}}{3}+\frac{{{v}_{2}}}{3}\] done
clear
C)
\[\frac{2{{v}_{1}}}{3}+\frac{{{v}_{2}}}{3}\] done
clear
D)
\[{{v}_{1}}+\frac{2{{v}_{2}}}{3}\] done
clear
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question_answer14)
A particle moves in straight line with velocity \[6\text{ }m/s\]and \[\text{3 }m/s\] for time intervals which are in ratio 1:2. Find average velocity.
A)
\[2\,\,m/s\] done
clear
B)
\[3\,\,m/s\] done
clear
C)
\[4\,\,m/s\] done
clear
D)
\[5\,\,m/s\] done
clear
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question_answer15)
A particle moves from (2, 3) m to (4, 1) m. The magnitude of displacement is
A)
\[2\text{ }m\] done
clear
B)
\[2\sqrt{3}\,\,m\] done
clear
C)
\[2\sqrt{2}\,\,m\] done
clear
D)
\[3\sqrt{2}\,\,m\] done
clear
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question_answer16)
Which of the following is not possible for a body in uniform motion?
A)
B)
C)
Both [a] & [b] done
clear
D)
None of these done
clear
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question_answer17)
A man leaves his house for a cycle ride. He comes back to his house after half-an-hour after covering a distance of one km. What is his average velocity for the ride?
A)
Zero done
clear
B)
\[2\,km\text{ }{{h}^{-1}}\] done
clear
C)
\[10\,km\text{ }{{s}^{-1}}\] done
clear
D)
\[\frac{1}{2}\,km\text{ }{{s}^{-1}}\] done
clear
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question_answer18)
A point traversed half of the distance with a velocity \[{{v}_{0}}\]. The half of remaining part of the distance was covered with velocity \[{{v}_{1}}\] and second half of remaining part by \[{{v}_{2}}\] velocity. The mean velocity of the point, averaged over the whole time of motion is
A)
\[\frac{{{\text{v}}_{\text{0}}}\text{+}{{\text{v}}_{1}}+{{\text{v}}_{2}}}{3}\] done
clear
B)
\[\frac{\text{2}{{\text{v}}_{\text{0}}}\text{+}{{\text{v}}_{1}}+{{\text{v}}_{2}}}{3}\] done
clear
C)
\[\frac{{{\text{v}}_{\text{0}}}\text{+.2}{{\text{v}}_{1}}+2{{\text{v}}_{2}}}{3}\] done
clear
D)
\[\frac{{{\text{v}}_{\text{0}}}\text{+2(}{{\text{v}}_{1}}+{{\text{v}}_{2}})}{\text{(2}{{\text{v}}_{\text{0}}}\text{+}{{\text{v}}_{1}}+{{\text{v}}_{2}})}\] done
clear
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question_answer19)
If a car covers \[2/5th\] of the total distance with \[{{v}_{1}}\] speed and \[3/5th\] distance with \[{{v}_{2}}\] then average speed is
A)
\[\frac{1}{2}\sqrt{{{\text{v}}_{1}}{{\text{v}}_{2}}}\] done
clear
B)
\[\frac{{{\text{v}}_{1}}+{{\text{v}}_{2}}}{2}\] done
clear
C)
\[\frac{2{{\text{v}}_{1}}{{\text{v}}_{2}}}{{{\text{v}}_{1}}+{{\text{v}}_{2}}}\] done
clear
D)
\[\frac{\text{5}{{\text{v}}_{1}}{{\text{v}}_{2}}}{\text{3}{{\text{v}}_{1}}+2{{\text{v}}_{2}}}\] done
clear
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question_answer20)
A person moves 30 m north and then 20 m towards east and finally \[30\sqrt{2}\] m south-west direction. The displacement of the person from the origin
A)
10 m along north done
clear
B)
10 m along south done
clear
C)
10 m along west done
clear
D)
Zero done
clear
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question_answer21)
A bus travelling the first one third distance at a speed of 10 km/h, the next one third at 20 km/h and the last one-third at 60 km/h. The average speed of the bus is
A)
9 km/h done
clear
B)
16 km/h done
clear
C)
18 km/h done
clear
D)
48 km/h done
clear
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question_answer22)
A bird flies with a speed of 10 km/h and a car moves with uniform speed of 8 km/h. Both start from B towards A (BA = 40 km) at the same instant. The bird having reached A, flies back immediately to meet the approaching car. As soon as it reaches the car, it flies back to A. The bird repeats this till both the car and the bird reach A simultaneously. The total distance flown by the bird is
A)
80 km done
clear
B)
40 km done
clear
C)
50 km done
clear
D)
30 km done
clear
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question_answer23)
A car moves with a speed of 60 km/hr from point A to point B and then with the speed of 40 km/hr from point B to point C. Further it moves to a point D with a speed equal to its average speed between A and C. Points A, B, C and D are collinear and equidistant. The average speed of the car between A and D is
A)
\[30\text{ }km/hr\] done
clear
B)
\[50\text{ }km/hr\] done
clear
C)
\[\text{48 }km/hr\] done
clear
D)
\[\text{60 }km/hr\] done
clear
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question_answer24)
Three elephants A, B and C are moving along a straight line with constant speed in same direction as shown in figure. Speed of A is \[5\text{ }m/s\] and speed of C is 10 m/s. Initially separation between A and B is 'd' and between B and C is also. When 'B' catches 'C' separation between A and C becomes 3d. Then the speed of B will be
A)
\[7.5\text{ }m/s\] done
clear
B)
\[15\text{ }m/s\] done
clear
C)
\[\text{20 }m/s\] done
clear
D)
\[\text{5 }m/s\] done
clear
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question_answer25)
If a body travels with constant acceleration, which of the following quantities remains constant?
A)
Displacement done
clear
B)
Velocity done
clear
C)
Time done
clear
D)
None of these done
clear
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question_answer26)
A bus starts moving with acceleration \[2\text{ }m/{{s}^{2}}\]. A cyclist 96 m behind the bus starts simultaneously towards the bus at 20 m/s. After what time will he be able to overtake the bus?
A)
4 sec done
clear
B)
8 sec done
clear
C)
18 sec done
clear
D)
16 sec done
clear
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question_answer27)
The velocity time graph of the motion of the body is as shown below
The total distance travelled by the body during the motion is equal to __.
A)
\[\frac{\text{1}}{\text{2}}\left( \text{AD+BE} \right)\text{ }\!\!\times\!\!\text{ OC}\] done
clear
B)
\[\frac{\text{1}}{\text{2}}\left( \text{OA+BC} \right)\text{ }\!\!\times\!\!\text{ OC}\] done
clear
C)
\[\frac{\text{1}}{\text{2}}\left( \text{OC+AB} \right)\text{ }\!\!\times\!\!\text{ AD}\] done
clear
D)
\[\frac{\text{1}}{\text{2}}\left( \text{OA+AB} \right)\text{ }\!\!\times\!\!\text{ BC}\] done
clear
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question_answer28)
Stopping distance of a moving vehicle is directly proportional to
A)
square of the initial velocity done
clear
B)
square of the initial acceleration done
clear
C)
the initial velocity done
clear
D)
the initial acceleration done
clear
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question_answer29)
Which of the following graphs gives the equation \[\text{x = }{{\text{v}}_{0}}\text{t+}\frac{1}{2}\text{ a}{{\text{t}}^{2}}\]
A)
B)
C)
D)
None of these done
clear
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question_answer30)
The displacement of a particle is represented by the following equation: \[S=3{{t}^{3}}+7{{t}^{2}}+5t+8\] where S is in meter and t in second. The acceleration of the particle at t = 15 is
A)
\[14\,\,m/{{s}^{2}}\] done
clear
B)
\[18\,\,m/{{s}^{2}}\] done
clear
C)
\[32\,\,m/{{s}^{2}}\] done
clear
D)
Zero done
clear
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question_answer31)
If a train travelling at \[20\text{ }m/s\] is to be brought to rest in a distance of 200 m, then its retardation should be
A)
\[1\text{ }m/{{s}^{2}}\] done
clear
B)
\[2\text{ }m/{{s}^{2}}\] done
clear
C)
\[10\text{ }m/{{s}^{2}}\] done
clear
D)
\[20\text{ }m/{{s}^{2}}\] done
clear
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question_answer32)
The distance travelled by a particle starting from rest and moving with an acceleration \[\frac{4}{3}\text{m}{{\text{s}}^{-2}}\], in the third second is:
A)
6 m done
clear
B)
4 m done
clear
C)
\[\frac{10}{3}\,m\] done
clear
D)
\[\frac{19}{3}\,m\] done
clear
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question_answer33)
If a car at rest accelerates uniformly to a speed of 144 km/h in 20 s, it covers a distance of
A)
2880 m done
clear
B)
1440 m done
clear
C)
400 m done
clear
D)
20 m done
clear
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question_answer34)
The displacement x of a particle along a straight line at time t is given by: \[\text{x = }{{\text{a}}_{\text{0}}}\text{+}\frac{{{\text{a}}_{\text{1}}}\text{t}}{\text{2}}\text{+}\frac{{{\text{a}}_{\text{2}}}}{\text{3}}{{\text{t}}^{\text{2}}}\]. The acceleration of the particle is
A)
\[\frac{{{a}_{2}}}{3}\] done
clear
B)
\[\frac{2{{a}_{2}}}{3}\] done
clear
C)
\[\frac{{{a}_{1}}}{2}\] done
clear
D)
\[{{a}_{0}}+\frac{{{a}_{2}}}{3}\] done
clear
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question_answer35)
The dependence of velocity of a body with time is given by the equation \[v=20+0.\text{ }1\text{ }{{t}^{2}}\]. The body is in
A)
uniform retardation done
clear
B)
uniform acceleration done
clear
C)
non-uniform acceleration done
clear
D)
zero acceleration. done
clear
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question_answer36)
A car accelerates from rest at a constant rate \[\alpha \] for some time, after which it decelerates at a constant rate \[\beta \] and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is
A)
\[\left( \frac{{{\alpha }^{2}}+{{\beta }^{2}}}{\alpha \beta } \right)\text{t}\] done
clear
B)
\[\left( \frac{{{\alpha }^{2}}-{{\beta }^{2}}}{\alpha \beta } \right)\] done
clear
C)
\[\frac{\left( {{\alpha }^{{}}}+{{\beta }^{{}}} \right)\text{t}}{\alpha \beta }\] done
clear
D)
\[\frac{\alpha \beta \text{t}}{{{\alpha }^{{}}}+{{\beta }^{{}}}}\] done
clear
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question_answer37)
The deceleration experienced by a moving motorboat after its engine is cut off, is given by \[\frac{\text{dv}}{\text{dt}}\text{ = -K}{{\text{V}}^{3}}\] where K is constant. If \[{{V}_{0}}\] is the magnitude of the velocity at cut-off, the magnitude of the velocity at a time t after the cut-off is
A)
\[\frac{{{V}_{0}}}{\sqrt{\left( 2V_{0}^{2}Kt+1 \right)}}\] done
clear
B)
\[{{V}_{0}}{{e}^{-Kt}}\] done
clear
C)
\[{{V}_{0}}/2\] done
clear
D)
\[{{V}_{0}}\] done
clear
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question_answer38)
The displacement of a particle as a function of time is shown in figure. It indicates that
A)
the velocity of the particle is constant throughout done
clear
B)
the acceleration of the particle is constant throughout done
clear
C)
the particle starts with a constant velocity and is accelerated done
clear
D)
the motion is retarded and finally the particle stops done
clear
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question_answer39)
A particle moves along a straight line OX. At a time t (in second) the distance x (in metre) of the particle from O is given by \[x=40+12t-{{t}^{3}}\]. How long would the particle travel before coming to rest?
A)
24 m done
clear
B)
40 m done
clear
C)
56 m done
clear
D)
16 m done
clear
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question_answer40)
A particle moves a distance x in time t according to equation \[x={{\left( t+5 \right)}^{-1}}\]. The acceleration of particle is proportional to
A)
\[{{\left( velocity \right)}^{3/2}}\] done
clear
B)
\[{{\left( distance \right)}^{2}}\] done
clear
C)
\[{{\left( distance \right)}^{-2}}\] done
clear
D)
\[{{\left( velocity \right)}^{2/3}}\] done
clear
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question_answer41)
A particle is moving eastwards with a velocity of \[5\text{ }m{{s}^{-1}}\]. In 10 seconds the velocity changes to \[5\text{ }m{{s}^{-1}}\] northwards. The average acceleration in this time is
A)
\[\frac{1}{2}m{{s}^{-2}}\] toward north done
clear
B)
\[\frac{1}{\sqrt{2}}m{{s}^{-2}}\] toward north-east done
clear
C)
\[\frac{1}{\sqrt{2}}m{{s}^{-2}}\] towards north-west done
clear
D)
zero done
clear
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question_answer42)
It is given that \[t=p{{x}^{2}}+qx\], where x is displacement and t is time. The acceleration of particle at origin is
A)
\[-\frac{2\text{p}}{{{\text{q}}^{3}}}\] done
clear
B)
\[-\frac{2\text{q}}{{{\text{p}}^{3}}}\] done
clear
C)
\[\frac{2\text{p}}{{{\text{q}}^{3}}}\] done
clear
D)
\[\frac{2\text{q}}{{{\text{p}}^{3}}}\] done
clear
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question_answer43)
An object, moving with a speed of \[6.25\text{ }m/s\], is decelerate data rate given by: \[\frac{\text{dv}}{\text{dt}}=\text{ -2}\text{.5}\sqrt{\text{v}}\]where v is the instantaneous speed. The time taken by the object, to come to rest, would be
A)
2s done
clear
B)
4s done
clear
C)
8s done
clear
D)
1s done
clear
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question_answer44)
A bike accelerates from rest at a constant rate \[5\,\,m/{{s}^{2}}\] for some time after which it decelerates at a constant rate \[3\text{ }m/{{s}^{2}}\] to come to rest. If the total time elapsed is 8 second, the maximum velocity acquired by the bike is given by
A)
5 m/s done
clear
B)
10 m/s done
clear
C)
12 m/s done
clear
D)
15 m/s done
clear
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question_answer45)
A metro train starts from rest and in 5 s achieves 108 km/h. After that it moves with constant velocity and comes to rest after travelling 45 m with uniform retardation. If total distance travelled is 395 m, find total time of travelling.
A)
12.2s done
clear
B)
15.3s done
clear
C)
9s done
clear
D)
17.2s done
clear
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question_answer46)
A car, starting from rest, accelerates at the rate through a distance S, then continues at constant speed for time t and then decelerates at the rate \[\frac{\text{f}}{2}\]to come to rest. If the total distance traversed is 15 S, then
A)
\[\text{S=}\frac{\text{1}}{\text{6}}\text{f}{{\text{t}}^{\text{2}}}\] done
clear
B)
\[\text{S=ft}\] done
clear
C)
\[\text{S=}\frac{\text{1}}{\text{4}}\text{f}{{\text{t}}^{\text{2}}}\] done
clear
D)
\[\text{S=}\frac{\text{1}}{\text{72}}\text{f}{{\text{t}}^{\text{2}}}\] done
clear
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question_answer47)
A particle starting with certain initial velocity and uniform acceleration covers a distance of 12 m in first 3 seconds and a distance of 30 m in next 3 seconds. The initial velocity of the particle is
A)
\[3\text{ }m{{s}^{-1}}\] done
clear
B)
\[2.5\text{ }m{{s}^{-1}}\] done
clear
C)
\[2\text{ }m{{s}^{-1}}\] done
clear
D)
\[\text{1 }m{{s}^{-1}}\] done
clear
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question_answer48)
The velocity of an object moving rectilinearly is given as a function of time by \[v=4t-3{{t}^{2}},\] where v is in m/s and t is in seconds. The average velocity of particle between t = 0 to t = 2 seconds is
A)
\[0\] done
clear
B)
\[-2\text{ }m/s\] done
clear
C)
\[-4\text{ }m/s\] done
clear
D)
\[\text{8 }m/s\] done
clear
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question_answer49)
A body starts from rest and is uniformly accelerated for 30 s. The distance travelled in the first 10 s is \[{{x}_{1}}\], next 10 s is \[{{x}_{2}}\], and the last 10 s is \[{{x}_{3}}\]. Then \[{{x}_{1}}:\text{ }{{x}_{2}}:\text{ }{{x}_{3}}\] is the same as:
A)
1:2:4 done
clear
B)
1:2:5 done
clear
C)
1:3:5 done
clear
D)
1:3:9 done
clear
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question_answer50)
The acceleration of a particle, starting from rest, varies with time according to the relation\[\text{a}=-\text{s}{{\omega }^{2}}\sin \omega \text{t}\]. The displacement of this particle at a time t will be
A)
\[\text{s sin }\omega \text{ t}\] done
clear
B)
\[\text{s }\omega \text{ cos }\omega \text{ t}\] done
clear
C)
\[\text{s }\omega \text{ sin}\omega \text{t}\] done
clear
D)
\[-\frac{1}{2}\left( \text{s}{{\omega }^{2}}\text{ sin }\omega \text{t} \right){{\text{t}}^{2}}\] done
clear
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question_answer51)
A particle is moving along a straight line path according to the relation \[{{s}^{2}}=a{{t}^{2}}+2bt+c\] s represents the distance travelled in t seconds and a, b, c are constants. Then the acceleration of the particle varies as
A)
\[{{s}^{-\,3}}\] done
clear
B)
\[{{s}^{3/2}}\] done
clear
C)
\[{{s}^{-2/3}}\] done
clear
D)
\[{{s}^{2}}\] done
clear
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question_answer52)
A car of mass 1000 kg is moving at a speed of 30 m/s. Brakes are applied to bring the car to rest. If the deceleration is \[5\text{ }m/{{s}^{2}}\] the car comes to stop after travelling d m in t s. Then
A)
d = 150, t=5 done
clear
B)
d = 120, t=5 done
clear
C)
d = 180, t=6 done
clear
D)
d = 90, t=6 done
clear
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question_answer53)
A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity u and the guard's room passes with velocity v. The middle wagon of the train passes the pole with a velocity.
A)
\[\frac{\text{u+v}}{2}\] done
clear
B)
\[\frac{1}{2}\sqrt{{{\text{u}}^{\text{2}}}\text{+}{{\text{v}}^{\text{2}}}}\] done
clear
C)
\[\sqrt{\text{uv}}\] done
clear
D)
\[\sqrt{\left( \frac{{{\text{u}}^{2}}+{{\text{v}}^{2}}}{2} \right)}\] done
clear
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question_answer54)
Starting from rest a particle moves in a straight line with acceleration \[a={{(25-{{t}^{2}})}^{1/2}}m/{{s}^{2}}\] for \[0\le t\le \text{ }5s\], \[a=\frac{3\pi }{8}m/{{s}^{2}}\] for \[t>5s\]. The velocity of particle at \[t=7s\] is:
A)
11 m/s done
clear
B)
22 m/s done
clear
C)
33 m/s done
clear
D)
44 m/s done
clear
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question_answer55)
A car accelerates from rest with a constant acceleration \[\alpha \] on a straight road. After gaining a velocity \[{{v}_{1}}\], the car moves with the same velocity for some-time. Then the car decelerated to rest with a retardation \[\beta \]. If the total distance covered by the car is equal to S, the total time taken for its motion is
A)
\[\frac{S}{v}+\frac{v}{2}\left( \frac{1}{\alpha }+\frac{1}{\beta } \right)\] done
clear
B)
\[\frac{S}{v}+\frac{v}{\alpha }+\frac{v}{\beta }\] done
clear
C)
\[\left( \frac{v}{\alpha }+\frac{v}{\beta } \right)\] done
clear
D)
\[\frac{S}{v}-\frac{v}{2}\left( \frac{v}{\alpha }+\frac{1}{\beta } \right)\] done
clear
View Solution play_arrow
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question_answer56)
A truck has to carry a load in the shortest time from one station to another station situated at a distance L from the first. It can start up or slowdown at the same acceleration or deceleration what maximum velocity must the truck attain to satisfy this condition?
A)
\[\sqrt{La}\] done
clear
B)
\[\sqrt{2La}\] done
clear
C)
\[\sqrt{3La}\] done
clear
D)
\[\sqrt{5La}\] done
clear
View Solution play_arrow
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question_answer57)
Two trains, each 40 m long are travelling in opposite direction with equal velocity 20 m/s. The time of crossing is
A)
1s done
clear
B)
2s done
clear
C)
3s done
clear
D)
Zero done
clear
View Solution play_arrow
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question_answer58)
The graph shown below represent
A)
A and B are moving with same velocity in opposite directions done
clear
B)
velocity of B is more than A in same direction done
clear
C)
velocity of A is more than B in same direction done
clear
D)
velocity of A and B is equal in same direction done
clear
View Solution play_arrow
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question_answer59)
Two cars A and B approach each other at the same speed, then what will be the velocity of A if velocity of B is 8 m/s?
A)
16 m/s done
clear
B)
8 m/s done
clear
C)
-8 m/s done
clear
D)
Can't be determined. done
clear
View Solution play_arrow
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question_answer60)
A train of 150 m length is going towards north direction at a speed of \[10\text{ }m{{s}^{-1}}\]. A parrot flies at a speed of \[5\text{ }m{{s}^{-1}}\] towards south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to
A)
12s done
clear
B)
8s done
clear
C)
15s done
clear
D)
16s done
clear
View Solution play_arrow
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question_answer61)
A boat takes 2 hours to travel 8 km and back in Still Water Lake. With water velocity of \[4\,\,km\,\,{{h}^{-1}}\], the time taken for going upstream of 8 km and coming back is
A)
160 minutes done
clear
B)
80 minutes done
clear
C)
100 minutes done
clear
D)
120 minutes done
clear
View Solution play_arrow
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question_answer62)
Two trains are each 50 m long moving parallel towards each other at speeds \[10\text{ }m/s\] and 15 m/s respectively. After what time will they pass each other?
A)
\[5\sqrt{\frac{2}{3}}sec\] done
clear
B)
\[4\text{ }sec\] done
clear
C)
\[\text{2 }sec\] done
clear
D)
\[\text{6 }sec\] done
clear
View Solution play_arrow
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question_answer63)
A ship A is moving Westwards with a speed of \[10\text{ }km\text{ }{{h}^{-1}}\] and a ship B 100 km South of A, is moving Northwards with a speed of \[10\text{ }km\text{ }{{h}^{-1}}\]. The time after which the distance between them becomes shortest, is
A)
5h done
clear
B)
\[5\sqrt{2}\,\,h\] done
clear
C)
\[10\sqrt{2}\,h\] done
clear
D)
0 h done
clear
View Solution play_arrow
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question_answer64)
A bus is moving with a velocity of \[10\text{ }m{{s}^{-1}}\] on a straight road. A scootorist wishes to overtake the bus in one minute. If the bus is at a distance of 1.2 km ahead, then the velocity with which he has to chase the bus is
A)
\[20\,m{{s}^{-1}}\] done
clear
B)
\[25\,m{{s}^{-1}}\] done
clear
C)
\[60\,m{{s}^{-1}}\] done
clear
D)
\[30\,m{{s}^{-1}}\] done
clear
View Solution play_arrow
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question_answer65)
Two particles P and Q simultaneously start moving from point A with velocities 15 m/s and 20 m/s respectively. The two particles move with acceleration equal in magnitude but opposite in direction. When P overtakes Q at B then its velocity is 30 m/s The velocity of Q at point B will be
A)
30 m/s done
clear
B)
5 m/s done
clear
C)
20 m/s done
clear
D)
15 m/s done
clear
View Solution play_arrow
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question_answer66)
A body A begins to move with initial velocity 2 m/sec and continue to moves at a constant acceleration \[a.\text{ }\Delta \text{t}=10\] seconds after the body A begins to move a body B departs from the same point with an initial velocity 12 m/sec and moves with the same acceleration a. What is the maximum acceleration a at which the body B can overtake A?
A)
\[1\text{ }m/{{s}^{2}}\] done
clear
B)
\[2\,m/{{s}^{2}}\] done
clear
C)
\[1/2\text{ }m/{{s}^{2}}\] done
clear
D)
\[3\text{ }m/{{s}^{2}}\] done
clear
View Solution play_arrow
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question_answer67)
Two particles start moving from rest from the same point along the same straight line. The first moves with constant velocity v and the second with constant acceleration a. During the time that elapse before the second catches the first, the greatest distance between the particles is
A)
\[\frac{{{\text{v}}^{2}}}{a}\] done
clear
B)
\[\frac{{{v}^{2}}}{2a}\] done
clear
C)
\[\frac{\text{2}{{\text{v}}^{2}}}{a}\] done
clear
D)
\[\frac{{{\text{v}}^{2}}}{4a}\] done
clear
View Solution play_arrow
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question_answer68)
A man travelling in a car with a maximum on stat speed of 20m/s watches the friend start off at a distance 100m ahead on a motor cycle with constant acceleration 'a'. The maximum value of 'a' for which the man in the car can reach his friend is
A)
\[2\text{ }m/{{s}^{2}}\] done
clear
B)
\[\text{1 }m/{{s}^{2}}\] done
clear
C)
\[4\text{ }m/{{s}^{2}}\] done
clear
D)
\[8\text{ }m{{s}^{-2}}\] done
clear
View Solution play_arrow
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question_answer69)
A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is [assume no air resistance close to earth]
A)
equal to the time of fall done
clear
B)
less than the time of fall done
clear
C)
greater than the time of fall done
clear
D)
twice the time of fall done
clear
View Solution play_arrow
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question_answer70)
A body is thrown upwards and reaches half of its maximum height. At that position
A)
its acceleration is minimum done
clear
B)
its velocity is maximum done
clear
C)
its velocity is zero done
clear
D)
its acceleration is constant done
clear
View Solution play_arrow
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question_answer71)
A ball thrown vertically upwards after reaching a maximum height h, returns to the starting point after a time of 10 s. Its displacement is
A)
h done
clear
B)
2 h done
clear
C)
10 h done
clear
D)
zero done
clear
View Solution play_arrow
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question_answer72)
The ball is projected up from ground with speed \[30\text{ }m/sec\]. What is the average velocity for time 0 to 4 sec?
A)
\[10\text{ }m/sec\] done
clear
B)
\[20\text{ }m/sec\] done
clear
C)
\[\text{15 }m/sec\] done
clear
D)
\[zero\] done
clear
View Solution play_arrow
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question_answer73)
A body is projected vertically upwards. If \[{{t}_{1}}\] and \[{{t}_{2}}\] be the times at which it is at height h above the projection while ascending and descending respectively, then h is
A)
\[\frac{1}{2}g{{t}_{1}}{{t}_{2}}\] done
clear
B)
\[g\,{{t}_{1}}{{t}_{2}}\] done
clear
C)
\[2g\,{{t}_{1}}{{t}_{2}}\] done
clear
D)
\[2hg\] done
clear
View Solution play_arrow
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question_answer74)
Two balls A and B of same mass are thrown from the top of the building. A thrown upward with velocity v and B, thrown down with velocity v, hen
A)
velocity A is more than B at the ground done
clear
B)
velocity of B is more than A at the ground done
clear
C)
both A & B strike the ground with same velocity done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer75)
A rocket is fired upward from the earth's surface such that it creates an acceleration of \[19.6\,\,m{{s}^{-2}}\]. If after 5 s, its engine is switched off, the maximum height of the rocket from earth's surface would be
A)
980 m done
clear
B)
735 m done
clear
C)
490 m done
clear
D)
245 m done
clear
View Solution play_arrow
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question_answer76)
A man throws balls with same speed vertically upwards one after the other at an interval of 2 sec. What should be the speed of throw so that more man two balls are in air at any time?
A)
Only with speed 19.6 m/s done
clear
B)
More than 19.6 m/s done
clear
C)
At least 9.8 m/s done
clear
D)
Any speed less than 19.6 m/s. done
clear
View Solution play_arrow
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question_answer77)
A stone is dropped from a rising balloon at a height of 76 m above the ground and reaches the ground in 6s. What was the velocity of the balloon when the stone was dropped? Take \[g=10\text{ }m/{{s}^{2}}\]
A)
\[\frac{52}{3}\,m/s\] upward done
clear
B)
\[\frac{52}{3}\,m/s\] downward done
clear
C)
\[3\text{ }m/s\] done
clear
D)
\[9.8\text{ }m/s\] done
clear
View Solution play_arrow
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question_answer78)
Let A, B, C, D be points on a vertical line such that AB = BC = CD. If a body is released from position A, the times of descent through AB, BC and CD are in the ratio.
A)
\[1:\sqrt{3}-\sqrt{2}:\sqrt{3}+\sqrt{2}\] done
clear
B)
\[1:\sqrt{2}-1:\sqrt{3}-\sqrt{2}\] done
clear
C)
\[1:\sqrt{2}-1:\sqrt{3}\] done
clear
D)
\[1:\sqrt{2}:\sqrt{3}-1\] done
clear
View Solution play_arrow
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question_answer79)
If two balls of masses \[{{m}_{1}}\] and \[{{m}_{2}}({{m}_{1}}=2{{m}_{2}})\] are dropped from the same height, then the ratio of the time taken by them to reach the ground will be
A)
\[{{m}_{1}}:{{m}_{2}}\] done
clear
B)
\[2{{m}_{2}}:{{m}_{1}}\] done
clear
C)
1 : 1 done
clear
D)
1 : 2 done
clear
View Solution play_arrow
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question_answer80)
A boy standing at the top of a tower of 20 m height drops a stone. Assuming \[g=10\text{ }m{{s}^{-2}}\], the velocity with which it hits the ground is
A)
\[10.0\,m/s\] done
clear
B)
\[20.0\,m/s\] done
clear
C)
\[40.0\,m/s\] done
clear
D)
\[5.0\,m/s\] done
clear
View Solution play_arrow
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question_answer81)
What will be the ratio of the distances moved by a freely falling body from rest on 4th and 5th seconds of journey?
A)
4 : 5 done
clear
B)
7 : 9 done
clear
C)
16 : 25 done
clear
D)
1 : 1 done
clear
View Solution play_arrow
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question_answer82)
From a balloon moving upwards with a velocity of \[12\text{ }m{{s}^{-1}}\], a packet is released when it is at a height of 65 m from the ground. 7 lie time taken by it to reach the ground is \[(g=10\text{ }m{{s}^{-2}})\]
A)
5s done
clear
B)
8s done
clear
C)
4s done
clear
D)
7s done
clear
View Solution play_arrow
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question_answer83)
A ball dropped from a point A falls down vertically to C, through the midpoint B. The descending time from A to B and that from A to C are in the ratio
A)
1 : 1 done
clear
B)
1 : 2 done
clear
C)
1 : 3 done
clear
D)
\[1:\sqrt{2}\] done
clear
View Solution play_arrow
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question_answer84)
A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18s. What is the value of v? \[(take\text{ }g=10\text{ }m/{{s}^{2}})\]
A)
75 m/s done
clear
B)
55 m/s done
clear
C)
40 m/s done
clear
D)
60 m/s done
clear
View Solution play_arrow
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question_answer85)
A stone falls freely under gravity. It covers distances \[{{h}_{1}},\,\,{{h}_{2}}\] and \[{{h}_{3}}\] in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between \[{{h}_{1}},\,\,{{h}_{2}}\] and \[{{h}_{3}}\] is
A)
\[{{h}_{1}}=\frac{{{h}_{2}}}{3}=\frac{{{h}_{3}}}{5}\] done
clear
B)
\[{{h}_{2}}=3{{h}_{1}}\text{ }and\text{ }{{h}_{3}}=3{{h}_{2}}\] done
clear
C)
\[{{h}_{1}}={{h}_{2}}={{h}_{3}}\] done
clear
D)
\[{{h}_{1}}=2{{h}_{2}}=3{{h}_{3}}\] done
clear
View Solution play_arrow
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question_answer86)
From a building two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically). If \[{{T}_{A}}\] and \[{{T}_{B}}\] are their respective time of flights then
A)
\[{{T}_{A}}>{{T}_{B}}\] done
clear
B)
\[{{T}_{A}}={{T}_{B}}\] done
clear
C)
\[{{T}_{A}}<{{T}_{B}}\] done
clear
D)
Their time of flights depend on their masses. done
clear
View Solution play_arrow
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question_answer87)
A ball is released from the top of tower of height h meter. It takes T second to reach the ground. What is the position in (m) from the ground of the ball in T/3 second?
A)
\[\frac{h}{9}\] done
clear
B)
\[\frac{7h}{9}\] done
clear
C)
\[\frac{8h}{9}\] done
clear
D)
\[\frac{17h}{18}\] done
clear
View Solution play_arrow
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question_answer88)
A stone is dropped into a well in which the level of water is h below the top of the well. If v is velocity of sound, the time T after which the splash is heard is given by
A)
\[T=2h/v\] done
clear
B)
\[\text{T=}\sqrt{\left( \frac{\text{2h}}{\text{g}} \right)\text{+}\frac{\text{h}}{\text{v}}}\] done
clear
C)
\[\text{T=}\sqrt{\left( \frac{\text{2h}}{\text{g}} \right)}\text{+}\frac{\text{h}}{\text{g}}\] done
clear
D)
\[\text{T=}\sqrt{\left( \frac{\text{h}}{\text{2g}} \right)}\text{+}\frac{\text{2h}}{\text{v}}\] done
clear
View Solution play_arrow
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question_answer89)
A ball is thrown vertically upwards. It was observed, at a height h twice with a time interval \[\Delta \,t\]. The initial velocity of the ball is
A)
\[\sqrt{8gh+{{g}^{2}}{{\left( \Delta \,t \right)}^{2}}}\] done
clear
B)
\[\sqrt{8gh+{{\left( \frac{g\Delta \,t}{2} \right)}^{2}}}\] done
clear
C)
\[\frac{1}{2}\sqrt{8gh+{{g}^{2}}{{\left( \Delta \,t \right)}^{2}}}\] done
clear
D)
\[\sqrt{8gh+4{{g}^{2}}{{\left( \Delta \,t \right)}^{2}}}\] done
clear
View Solution play_arrow
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question_answer90)
The balls are released from the top of a tower of height H at regular interval of time. When first ball reaches at the ground, the nth ball is to be just released and \[{{\left( \frac{\text{n+1}}{\text{2}} \right)}^{\text{th}}}\]ball is at same distance 'h' from top of the tower. The value of h is.
A)
\[\frac{2}{3}\,\,H\] done
clear
B)
\[\frac{3}{4}H\] done
clear
C)
\[\frac{4}{5}H\] done
clear
D)
\[\frac{5\,H}{6}\] done
clear
View Solution play_arrow
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question_answer91)
A ball is dropped from the top of a tower of height 100 m and at the same time another ball is projected vertically upwards from ground with a velocity \[25\text{ }m{{s}^{-1}}\]. Then the distance from the top of the tower, at which the two balls meet is
A)
68.4 m done
clear
B)
48.4 m done
clear
C)
18.4 m done
clear
D)
78.4 m done
clear
View Solution play_arrow
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question_answer92)
A body thrown vertically so as to reach its maximum height in t second. The total time from the time of projection to reach a point at half of its maximum height while returning (in sec) is
A)
\[\sqrt{\text{2}}\text{t}\] done
clear
B)
\[\left( \text{1+}\frac{\text{1}}{\sqrt{\text{2}}} \right)\text{t}\] done
clear
C)
\[\frac{\text{3t}}{\text{2}}\] done
clear
D)
\[\frac{\text{t}}{\sqrt{\text{2}}}\] done
clear
View Solution play_arrow
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question_answer93)
A body dropped from top of a tower fall through 40 m during the last two seconds of its fall. The height of tower is \[(g=10\text{ }m/{{s}^{2}})\]
A)
60 m done
clear
B)
45 m done
clear
C)
80 m done
clear
D)
50 m done
clear
View Solution play_arrow
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question_answer94)
From a pole of height 10 m, a stone is thrown vertically upwards with a speed 5 m/s. The time taken by the stone, to hit the ground, is n times that taken by it to reach the highest point of its path. The value of n is \[[take\text{ }g=10\text{ }m/{{s}^{2}}]\]
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
5 done
clear
View Solution play_arrow
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question_answer95)
A body A is thrown vertically upward with the initial velocity \[{{v}_{1}}\]. Another body B is dropped from a height h. Find how the distance x between the bodies depends on the time t if the bodies begin to move simultaneously.
A)
\[x=h-{{v}_{1}}t\] done
clear
B)
\[x=\left( h-{{v}_{1}} \right)t\] done
clear
C)
\[x=h-\frac{{{v}_{1}}}{t}\] done
clear
D)
\[x=\frac{h}{t}-{{v}_{1}}\] done
clear
View Solution play_arrow
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question_answer96)
A body is thrown upwards. If air resistance causing deceleration of \[5\text{ }m/{{s}^{2}}\], then ratio of time of ascent to time of descent is \[[take\text{ }g=10\text{ }m/{{s}^{2}}]\]
A)
\[\sqrt{\frac{1}{2}}\] done
clear
B)
\[\sqrt{\frac{1}{2.5}}\] done
clear
C)
\[\sqrt{\frac{1}{3}}\] done
clear
D)
\[\sqrt{\frac{1}{5}}\] done
clear
View Solution play_arrow
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question_answer97)
A particle when thrown, moves such that it passes from same height at 2 and 10 seconds, then this height h is:
A)
5g done
clear
B)
g done
clear
C)
8g done
clear
D)
10g done
clear
View Solution play_arrow
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question_answer98)
A hunter tries to hunt a monkey with a small, very poisonous arrow, blown from a pipe with initial speed \[{{v}_{0}}\]. The monkey is hanging on a branch of tree at height H above the ground. The hunter is at a distance L from the bottom of the tree. The monkey sees the arrow leaving the blow pipe and immediately loses the grip on the tree, falling freely down with zero initial velocity. The minimum initial speed \[{{v}_{0}}\] of the arrow for hunter to succeed while monkey is in air is
A)
\[\sqrt{\frac{g\left( {{H}^{2}}+{{L}^{2}} \right)}{2H}}\] done
clear
B)
\[\sqrt{\frac{g{{H}^{2}}}{\sqrt{{{H}^{2}}+{{L}^{2}}}}}\] done
clear
C)
\[\sqrt{\frac{g\sqrt{{{H}^{2}}+{{L}^{2}}}}{H}}\] done
clear
D)
\[\sqrt{\frac{2g{{H}^{2}}}{\sqrt{{{H}^{2}}+{{L}^{2}}}}}\] done
clear
View Solution play_arrow
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question_answer99)
A ball is dropped from the top of a building. The ball takes 0.5 s to fall past the 3 m length of a window some distance from the top of the building. If the velocities of the ball at the top and at the bottom of the window are \[{{v}_{T}}\] and \[{{v}_{B}}\] respectively, then \[(take\text{ }g=10\text{ }m/{{s}^{2}})\]
A)
\[{{\text{v}}_{\text{T}}}\text{+}{{\text{v}}_{\text{B}}}\text{=12m}{{\text{s}}^{-1}}\] done
clear
B)
\[{{\text{v}}_{\text{T}}}-{{\text{v}}_{\text{B}}}=4.9\text{m}{{\text{s}}^{-1}}\] done
clear
C)
\[{{\text{v}}_{\text{B}}}{{\text{v}}_{\text{T}}}\text{=1m}{{\text{s}}^{-1}}\] done
clear
D)
\[{{\text{v}}_{\text{B}}}\text{/}{{\text{v}}_{\text{T}}}\text{=1m}{{\text{s}}^{-1}}\] done
clear
View Solution play_arrow
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question_answer100)
From a building two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically). If \[{{v}_{A}}\] and \[{{v}_{B}}\] are their respective velocities on reaching the ground, then
A)
\[{{v}_{B}}>{{v}_{A}}\] done
clear
B)
\[{{v}_{A}}={{v}_{B}}\] done
clear
C)
\[{{v}_{A}}>{{v}_{B}}\] done
clear
D)
their velocities depend on their masses. done
clear
View Solution play_arrow