-
question_answer1)
A missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energy is
A)
Positive done
clear
B)
Negative done
clear
C)
Zero done
clear
D)
May be positive or negative depending upon its initial velocity done
clear
View Solution play_arrow
-
question_answer2)
A rocket of mass \[M\] is launched vertically from the surface of the earth with an initial speed \[V\] Assuming the radius of the earth to be \[R\] and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is
A)
\[R/\left( \frac{gR}{2{{V}^{2}}}-1 \right)\] done
clear
B)
\[{{R}_{{}}}\left( \frac{gR}{2{{V}^{2}}}-1 \right)\] done
clear
C)
\[R/\left( \frac{gR}{2{{V}^{2}}}-1 \right)\] done
clear
D)
\[R\left( \frac{2gR}{{{V}^{2}}}-1 \right)\] done
clear
View Solution play_arrow
-
question_answer3)
Suppose, the acceleration due to gravity at the Earth's surface is \[10\,m{{s}^{2}}\] and at the surface of Mars it is \[4.0\,m/{{s}^{2}}\].\[A\,60-kg\] passenger goes from the Earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of figure best represents the weight (net gravitational force) of the passenger as a function of time?
A)
A done
clear
B)
B done
clear
C)
C done
clear
D)
D done
clear
View Solution play_arrow
-
question_answer4)
The earth moves around the Sun in an elliptical orbit as shown Earth in the figure. The ratio\[OA/OB=x\]. The ratio of the speed of the earth at B to that at A is nearly
A)
\[\sqrt{x}\] done
clear
B)
\[x\] done
clear
C)
\[x\sqrt{x}\] done
clear
D)
\[{{x}^{2}}\] done
clear
View Solution play_arrow
-
question_answer5)
As observed from the earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from the earth, this would
A)
be similarly true done
clear
B)
not be true because the force between the earth and mercury is not inverse square law done
clear
C)
not be true because the major gravitational force on mercury is due to the sun done
clear
D)
not be true because mercury is influenced by forces other than gravitational forces done
clear
View Solution play_arrow
-
question_answer6)
A rubber of volume 2000 cc is alternately subjected to tension and released. The figure shows the stress-strain curve of rubber. Each curve is a quadrant of an ellipse. The. amount of energy lost as heat per cycle per unit volume will be
A)
\[\left( \frac{\pi }{2}-1 \right)\times 16\times {{10}^{2}}J\] done
clear
B)
\[\left( \frac{\pi }{4}-1 \right)\times 8\times {{10}^{2}}J\] done
clear
C)
\[\left( \frac{\pi }{4}-1 \right)\times 32\times {{10}^{2}}J\] done
clear
D)
\[\left( \frac{\pi }{2}-1 \right)\times 32\times {{10}^{2}}J\] done
clear
View Solution play_arrow
-
question_answer7)
Two wires are made of the same material and have the same volume. However, wire 1 has cross-sectional area \[A\] and wire 2 has cross-sectional area\[3A\]. If the length of wire 1 increases by Ax on applying a force \[F\], how much force is needed to stretch wire 2 by the same amount?
A)
\[F\] done
clear
B)
\[4F\] done
clear
C)
\[6F\] done
clear
D)
\[9F\] done
clear
View Solution play_arrow
-
question_answer8)
If the radius of the earth decreases by 10%, the mass remaining unchanged, what will happen to the acceleration due to gravity?
A)
Decreases by 19% done
clear
B)
Increases by 19% done
clear
C)
Decreases by more than 19% done
clear
D)
Increase by more than 19% done
clear
View Solution play_arrow
-
question_answer9)
Wires \[A\] and \[B\] are connected with blocks \[P\] and \[Q\], as shown. The ratio of lengths, radii and Young's modulus of wires \[A\] and \[B\] are \[r,\,2r\] and 3r respectively (\[r\] is a constant). Find the mass of block \[P\] if ratio of increase in their corresponding lengths is \[\frac{1}{6{{r}^{2}}}\]. The mass of the block \[Q\] is 3\[M\]
A)
\[M\] done
clear
B)
\[3M\] done
clear
C)
\[6M\] done
clear
D)
\[9M\] done
clear
View Solution play_arrow
-
question_answer10)
The ratio of diameters of two wires of same material is n: 1. The length of each wire is 4 m. On applying the same load, the increases in the length of the thin wire will be (n>\)
A)
\[{{n}^{2}}times\] done
clear
B)
\[{{n}^{{}}}times\] done
clear
C)
\[2{{n}^{{}}}times\] done
clear
D)
\[{{(2n+1)}^{{}}}times\] done
clear
View Solution play_arrow
-
question_answer11)
Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is 0.5 cm, the elongation (\[l\]) of each wireis\[{{Y}_{s}}(steel)=2.0\times {{10}^{11}}N/{{m}^{2}}\] \[{{Y}_{c}}(copper)=1.2\times {{10}^{11}}N/{{m}^{2}}\]
A)
\[{{l}_{s}}=0.75\,cm,\,{{l}_{c}}=1.25\,cm\] done
clear
B)
\[{{l}_{s}}=1.25\,cm,\,{{l}_{c}}=0.75\,cm\] done
clear
C)
\[{{l}_{s}}=0.25\,cm,\,{{l}_{c}}=0.75\,cm\] done
clear
D)
\[{{l}_{s}}=0.75\,cm,\,{{l}_{c}}=0.25\,cm\] done
clear
View Solution play_arrow
-
question_answer12)
A rectangular block of size \[10cm\times 8cm\times 5cm\] is kept in three different positions P, Q and R in turn as shown in the figure. In each case, the shaded area is rigidly fixed and a definite force F is applied tangentially to the opposite face to deform the block. The displacement of the upper face will be
A)
Same in all the three cases done
clear
B)
Maximum in \[P\] position done
clear
C)
Maximum in \[Q\] position done
clear
D)
Maximum in \[R\] position done
clear
View Solution play_arrow
-
question_answer13)
The length of an elastic string is \[a\] metre when the longitudinal tension is 4 N and \[b\] metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is
A)
\[a-b\] done
clear
B)
\[5b-4a\] done
clear
C)
\[2a-\frac{1}{4}a\] done
clear
D)
\[4a-3b\] done
clear
View Solution play_arrow
-
question_answer14)
A uniform ring of mass \[m\] and radius r is placed directly above a uniform sphere of mass \[M\] and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance \[r\sqrt{3}\]\[r\] as shown in the figure. The gravitational force exerted by the sphere on the ring will be
A)
\[\frac{GMm}{8{{r}^{2}}}\] done
clear
B)
\[\frac{GMm}{4{{r}^{2}}}\] done
clear
C)
\[\sqrt{3}\frac{GMm}{8{{r}^{2}}}\] done
clear
D)
\[\frac{GMm}{8{{r}^{2}}\sqrt{3}}\] done
clear
View Solution play_arrow
-
question_answer15)
In a cosmic event, suppose a planet heavier than the earth with mass KM (K > 1) and radius K'R (K > 1) passes through a path near the earth (M and R are the mass and radius of earth). At what closest distance from surface of planet, we are in danger of being thrown into space:
A)
\[{{\left[ \frac{2KGM}{g} \right]}^{1/2}}-\frac{1}{2}K'R\] done
clear
B)
\[{{\left[ \frac{KGM}{2g} \right]}^{1/2}}-\frac{1}{2}K'R\] done
clear
C)
\[{{\left[ \frac{KGM}{g} \right]}^{1/2}}-\frac{1}{2}K'R\] done
clear
D)
\[{{\left[ \frac{KGM}{g} \right]}^{1/2}}-K'R\] done
clear
View Solution play_arrow
-
question_answer16)
Two planets revolve with same angular velocity about a star. The radius of orbit of outer planet is twice the radius of orbit of the inner planet. If Tis time period of the revolution of outer planet, find the time in which inner planet will fall into the star. If it was suddenly stopped.
A)
\[\frac{T\sqrt{2}}{8}\] done
clear
B)
\[\frac{T\sqrt{2}}{16}\] done
clear
C)
\[\frac{T\sqrt{2}}{4}\] done
clear
D)
\[\frac{T\sqrt{2}}{32}\] done
clear
View Solution play_arrow
-
question_answer17)
A satellite moves eastwards very near the surface of the Earth in equatorial plane with speed (\[{{v}_{0}}\]). Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If \[R\]= radius of the Earth and \[\omega \]) be its angular speed of the Earth about its own axis. Then find the approximate difference in the two time period as observed on the Earth.
A)
\[\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}+{{R}^{2}}{{\omega }^{2}}}\] done
clear
B)
\[\frac{2\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\] done
clear
C)
\[\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\] done
clear
D)
\[\frac{2\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}+{{R}^{2}}{{\omega }^{2}}}\] done
clear
View Solution play_arrow
-
question_answer18)
Four particles, each of mass \[M\]and equidistant from each other, move along a circle of radius \[R\] under the action of their mutual gravitational attraction. The speed of each particle is
A)
\[\sqrt{\frac{GM}{R}(1+2\sqrt{2})}\] done
clear
B)
\[\frac{1}{2}\sqrt{\frac{GM}{R}(1+2\sqrt{2})}\] done
clear
C)
\[\sqrt{\frac{GM}{R}}\] done
clear
D)
\[\sqrt{2\sqrt{2}\frac{GM}{R}}\] done
clear
View Solution play_arrow
-
question_answer19)
If \[{{W}_{1}}\], \[{{W}_{2}}\] and \[{{W}_{3}}\] represent the work done in moving a particle from A to B along three different paths 1, 2 and 3, respectively, (as shown in the figure) in the gravitational field of a point mass m, find the correct relation between \[{{W}_{1}}\],\[{{W}_{2}}\] and \[{{W}_{3}}\].
A)
\[{{W}_{1}}>{{W}_{2}}>{{W}_{3}}\] done
clear
B)
\[{{W}_{1}}={{W}_{2}}={{W}_{3}}\] done
clear
C)
\[{{W}_{1}}<{{W}_{2}}<{{W}_{3}}\] done
clear
D)
\[{{W}_{2}}<{{W}_{1}}<{{W}_{3}}\] done
clear
View Solution play_arrow
-
question_answer20)
Two bodies of masses \[{{M}_{1}}\] and \[{{M}_{2}}\] are placed at a distance \[R\]apart. Then at the position where the gravitational field due to them is zero, the gravitational potential is
A)
\[-G\frac{\sqrt{{{M}_{1}}}}{R}\] done
clear
B)
\[-G\frac{\sqrt{{{M}_{2}}}}{R}\] done
clear
C)
\[-{{(\sqrt{{{M}_{1}}}+\sqrt{{{M}_{2}}})}^{2}}\frac{G}{R}\] done
clear
D)
\[-{{(\sqrt{{{M}_{1}}}-\sqrt{{{M}_{2}}})}^{2}}\frac{G}{R}\] done
clear
View Solution play_arrow
-
question_answer21)
A wire is suspended vertically. One of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire (in Joule) is _______ .
View Solution play_arrow
-
question_answer22)
Two rods of different materials having coefficients of linear expansion \[{{a}_{1}}\] and \[{{a}_{2}}\]and Young's moduli, \[{{Y}_{1}}\]and\[{{Y}_{2}}\], respectively, are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If \[{{a}_{1}}/{{a}_{2}}=2/3\], then the thermal stresses developed in the two rods are equal, provided \[{{Y}_{1}}/{{Y}_{2}}\] is equal to_______ .
View Solution play_arrow
-
question_answer23)
Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is\[(40/3\pi )\times {{10}^{6}}N/{{m}^{2}}\]. If\[g=10m{{s}^{-12}}\], then what should be the minimum radius (in mm) of the wire used if it is not to break?
View Solution play_arrow
-
question_answer24)
The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by\[{{100}^{0}}C\,(in\times {{10}^{8}}pa)\]is ______. (For steel Young's modulus is \[2\times {{10}^{11}}N{{m}^{-2}}\] and coefficient of thermal expansion is \[1.1\times {{10}^{-5}}{{K}^{-1}}\])
View Solution play_arrow
-
question_answer25)
Two spherical bodies of masses \[m\] and \[5M\]and radii \[R\] and 2\[R\], respectively, are released in free space with initial separation between their centres equal to 12R. If they attract each other by gravitational force only, then the distance covered by the smaller body just before collision is __R.
View Solution play_arrow