-
question_answer1)
If \[F=\frac{v}{C\ln (xb)}\], then
A)
F and v denote force and velocity, the dimensions of C are [MT] done
clear
B)
x denotes distance, the dimensions of b are [\[L_{{}}^{-1}\]] done
clear
C)
The dimension of \[\frac{v}{C}\] never be same as F done
clear
D)
The dimensions of x must be same as \[\frac{v}{cb}\] done
clear
View Solution play_arrow
-
question_answer2)
A bus travels distance \[x_{1}^{{}}\]when accelerates from rest at constant rate\[a_{2}^{{}}\]for some time and after that travels a distance\[x_{2}^{{}}\]when decelerates at a constant rate \[a_{2}^{{}}\]to come to rest. A student established a relation \[x_{1}^{{}}+x_{2}^{{}}=\frac{a_{1}^{{}}a_{2}^{{}}t_{{}}^{2}}{2(a_{1}^{{}}+a_{2}^{{}})}\] Choose the correct option(s).
A)
The relation is dimensionally correct done
clear
B)
The relation is dimensionally incorrect done
clear
C)
The relation may be dimensionally correct done
clear
D)
None of the above done
clear
View Solution play_arrow
-
question_answer3)
A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be
A)
\[92\pm 2s\] done
clear
B)
\[92\pm 5.0s\] done
clear
C)
\[92\pm 1.8s\] done
clear
D)
\[92\pm 3s\] done
clear
View Solution play_arrow
-
question_answer4)
If \[m,\text{ }e,\,\,{{\varepsilon }_{0}},\] h and c denote mass electron, charge of electron. Planck's constant and speed of light, respectively. The dimensions of \[\frac{me_{{}}^{4}}{\varepsilon _{0}^{2}h_{{}}^{3}c}\] are
A)
[\[M_{{}}^{0}L_{{}}^{0}T_{{}}^{-1}\]] done
clear
B)
[\[M_{{}}^{0}L_{{}}^{-1}T_{{}}^{-1}\]] done
clear
C)
[\[M_{{}}^{2}L_{{}}^{{}}T_{{}}^{-3}\]] done
clear
D)
[\[M_{{}}^{0}L_{{}}^{-1}T_{{}}^{0}\]] done
clear
View Solution play_arrow
-
question_answer5)
In a direct impact, loss in kinetic energy is given by \[\Delta K=\frac{M_{1}^{{}}M_{2}^{{}}}{2(M_{1}^{{}}+M_{2}^{{}})}.(V_{1}^{{}}-V_{2}^{{}})_{{}}^{2}(1-k_{{}}^{2})\] with usual notations (except k). The quantity k will have dimensional formula
A)
[\[M_{{}}^{0}L_{{}}^{2}T_{{}}^{-2}\]] done
clear
B)
[\[M_{{}}^{{}}L_{{}}^{{}}T_{{}}^{-1}\]] done
clear
C)
[\[M_{{}}^{0}L_{{}}^{0}T_{{}}^{0}\]] done
clear
D)
[\[M_{{}}^{0}L_{{}}^{{}}T_{{}}^{-1}\]] done
clear
View Solution play_arrow
-
question_answer6)
While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation \[g=4\pi _{{}}^{2}(l/T_{{}}^{2})\] will be
A)
2% done
clear
B)
4% done
clear
C)
7% done
clear
D)
10% done
clear
View Solution play_arrow
-
question_answer7)
Number of particles is given by \[n=-D\frac{{{n}_{2}}-{{n}_{1}}}{{{x}^{2}}-{{x}_{1}}}\] crossing a unit area perpendicular to X-axis in unit time, where\[n_{1}^{{}}\]and \[n_{2}^{{}}\] are number of particles per unit volume for the value of \[x_{{}}^{{}}\]meant to \[x_{2}^{{}}\] and \[x_{1}^{{}}\]. Find dimensions of D called as diffusion constant
A)
\[M_{0}^{{}}LT_{{}}^{2}\] done
clear
B)
\[M_{{}}^{0}L_{{}}^{2}T_{{}}^{-4}\] done
clear
C)
\[M_{{}}^{0}L_{{}}^{{}}T_{{}}^{-3}\] done
clear
D)
\[M_{{}}^{0}L_{{}}^{2}T_{{}}^{-1}\] done
clear
View Solution play_arrow
-
question_answer8)
Experiment shows that two perfectly neutral parallel metal plates separated by a small distance d attract each other via a very weak force, known as the Casimir force. The force per unit area of the plates, F, depends only on the Planck constant h, on the speed of light c, and on d. Which of the following has the best chance of being correct for F?
A)
\[F=\frac{hc}{d_{{}}^{2}}\] done
clear
B)
\[F=\frac{hc}{d_{{}}^{4}}\] done
clear
C)
\[F=\frac{hd_{{}}^{2}}{c}\] done
clear
D)
\[F=\frac{d_{{}}^{4}}{hc}\] done
clear
View Solution play_arrow
-
question_answer9)
The respective number of significant figures for the numbers 23.023, 0.0003, and 2.1 x \[10_{{}}^{-3}\] are
A)
5, 1, 2 done
clear
B)
5, 1, 5 done
clear
C)
5, 5, 2 done
clear
D)
4, 4, 2 done
clear
View Solution play_arrow
-
question_answer10)
The potential energy of a particle varies with distance \[\chi \] as \[U=\frac{Ax_{{}}^{1/2}}{x_{{}}^{2}+B}\] where A and B are constants. The dimensional formula for A x B is
A)
\[M_{{}}^{1}L_{{}}^{7/2}T_{{}}^{-2}\] done
clear
B)
\[M_{{}}^{1}L_{{}}^{1/2}T_{{}}^{-2}\] done
clear
C)
\[M_{{}}^{1}L_{{}}^{5/2}T_{{}}^{-2}\] done
clear
D)
\[M_{{}}^{1}L_{{}}^{9/2}T_{{}}^{-2}\] done
clear
View Solution play_arrow
-
question_answer11)
The relative density of a material of a body is found by weighing it first in air and then in water. If the weight of the body in air is \[W_{1}^{{}}\] = \[8.00\text{ }\pm \text{ }0.05\text{ }N\]and the weight in water is \[W_{2}^{{}}\] = \[6.00\text{ }\pm \text{ }0.05\] N, then the relative density \[\rho _{r}^{{}}=W_{1}^{{}}/(W_{1}^{{}}-W_{2}^{{}})\] With the maximum permissible error is
A)
\[4.00\text{ }\pm 0.62\]% done
clear
B)
\[4.00\text{ }\pm 0.82\]% done
clear
C)
\[4.00\text{ }\pm 3.2\]% done
clear
D)
\[4.00\text{ }\pm 5.62\]% done
clear
View Solution play_arrow
-
question_answer12)
If force F, acceleration a, and time T are taken as the fundamental physical quantities, the dimensions of length on this system of units, are
A)
\[FAT_{{}}^{2}\] done
clear
B)
FAT done
clear
C)
FT done
clear
D)
\[AT_{{}}^{2}\] done
clear
View Solution play_arrow
-
question_answer13)
Which of the following product of \[e,h,\mu ,G\](where \[\mu \]is the permeability) be taken so that the dimensions of the product are same as that of the speed of light?
A)
\[he_{{}}^{-2}\mu _{{}}^{-1}G_{{}}^{0}\] done
clear
B)
\[h_{{}}^{2}eG_{{}}^{0}\mu \] done
clear
C)
\[h_{{}}^{0}e_{{}}^{2}G_{{}}^{-1}\mu \] done
clear
D)
\[hGe_{{}}^{-2}\mu _{{}}^{0}\] done
clear
View Solution play_arrow
-
question_answer14)
The best method to reduce random error is
A)
To change the instrument used for measurement done
clear
B)
To take help of experienced observer done
clear
C)
To repeat the experiment many times and to take the average results done
clear
D)
None of the above done
clear
View Solution play_arrow
-
question_answer15)
The position of a particle at time \[t\]is given by the relation \[x(t)=(\frac{v_{0}^{{}}}{\alpha })(1-c_{{}}^{-\alpha t})\]where \[v_{0}^{{}}\] ls a constant and a > 0. The dimensions of \[v_{0}^{{}}\] and \[\alpha \] are respectively
A)
\[M_{{}}^{0}L_{{}}^{1}T_{{}}^{-1}and\,T_{{}}^{-1}\] done
clear
B)
\[M_{{}}^{0}L_{{}}^{1}T_{{}}^{0}and\,T_{{}}^{-1}\] done
clear
C)
\[M_{{}}^{0}L_{{}}^{1}T_{{}}^{-1}and\,LT_{{}}^{-2}\] done
clear
D)
\[M_{{}}^{0}L_{{}}^{1}T_{{}}^{-1}and\,LT_{{}}^{{}}\] done
clear
View Solution play_arrow
-
question_answer16)
A body travels uniformly a distance of\[(S+\Delta S)\] in a time \[(t\pm \Delta t)\]. What may be the condition so that body within the error limits move with a velocity \[(\frac{S}{t}\pm \frac{\Delta S}{\Delta t})\]?
A)
\[\frac{\Delta t}{t}+\frac{S(\Delta t)_{{}}^{2}}{(\Delta S)t_{{}}^{2}}=\pm 1\] done
clear
B)
\[\frac{\Delta t}{t}+\frac{S\Delta t_{{}}^{{}}}{\Delta St_{{}}^{{}}}=\pm 1\] done
clear
C)
\[\frac{\Delta t}{t}+\frac{(\Delta S)t_{{}}^{{}}}{S(\Delta t)_{{}}^{{}}}=\pm 1\] done
clear
D)
\[\frac{\Delta t}{t}+\frac{S_{{}}^{2}\Delta t_{{}}^{{}}}{(\Delta S)_{{}}^{2}t_{{}}^{{}}}=\pm 1\] done
clear
View Solution play_arrow
-
question_answer17)
Force F is given in terms of time \[t\] and distance \[x\] by F =A sin C\[t\] + B cos\[Dx\]. Then the dimensions of \[A/B\] and \[C/D\] are
A)
\[[M_{{}}^{0}L_{{}}^{0}T_{{}}^{0}],[M_{{}}^{0}L_{{}}^{0}T_{{}}^{-1}]\] done
clear
B)
\[[M_{{}}^{{}}L_{{}}^{{}}T_{{}}^{-2}],[M_{{}}^{0}L_{{}}^{-1}T_{{}}^{0}]\] done
clear
C)
\[[M_{{}}^{0}L_{{}}^{0}T_{{}}^{0}],[M_{{}}^{0}L_{{}}^{{}}T_{{}}^{-1}]\] done
clear
D)
\[[M_{{}}^{0}L_{{}}^{1}T_{{}}^{-1}],[M_{{}}^{0}L_{{}}^{0}T_{{}}^{0}]\] done
clear
View Solution play_arrow
-
question_answer18)
The dimension of \[{{e}^{2}}/4\pi {{\varepsilon }_{2}}hc,\] where \[e,{{\varepsilon }_{0}},h\] and c are electronic charge, electric permittivity, Planck's constant and velocity of light in vacuum, respectively, is
A)
\[[{{M}^{0}}{{L}^{0}}{{T}^{0}}]\] done
clear
B)
\[[{{M}^{1}}{{L}^{0}}{{T}^{0}}]\] done
clear
C)
\[[{{M}^{0}}{{L}^{1}}{{T}^{0}}]\] done
clear
D)
\[[{{M}^{0}}{{L}^{0}}{{T}^{1}}]\] done
clear
View Solution play_arrow
-
question_answer19)
A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides the main scale line?
A)
0.75 mm done
clear
B)
0.80 mm done
clear
C)
0.70mm done
clear
D)
0.50mm done
clear
View Solution play_arrow
-
question_answer20)
Suppose refractive index \[\mu \] is given as\[\mu =A+\frac{B}{\lambda _{{}}^{2}}\] where A and B are constants and \[\lambda \] is wavelength, then dimensions of B are same as that of
A)
Wavelength done
clear
B)
Volume done
clear
C)
Pressure done
clear
D)
Area done
clear
View Solution play_arrow
-
question_answer21)
To determine the Young's modulus of a wire, the formula is \[Y=\frac{F}{A}\times \frac{L}{\Delta L}\]; where L = length, A = area of cross- section of the wire, \[\Delta L\]= change in length of the wire when stretched with a force \[F\]. What is the conversion factor to change it from CGS to MKS system?
A)
0.1 done
clear
B)
0.2 done
clear
C)
0.3 done
clear
D)
0.4 done
clear
View Solution play_arrow
-
question_answer22)
The dimensional formula for a physical quantity \[x\] is\[[{{M}^{-1}}{{L}^{3}}{{T}^{-2}}]\]. The errors in measuring the quantities M, L, and F, respectively, are 2%, 3%, and 4%. What is the maximum percentage of error that occurs in measuring the quantity x?
A)
20 done
clear
B)
19 done
clear
C)
21 done
clear
D)
22 done
clear
View Solution play_arrow
-
question_answer23)
If the acceleration due to gravity is \[10m{{s}^{-2}}\] and the units of length and time are changed in kilometer and hour respectively, what is the numerical value of the acceleration?
A)
129800 done
clear
B)
130000 done
clear
C)
129600 done
clear
D)
128000 done
clear
View Solution play_arrow
-
question_answer24)
The wavelength associated with a moving particle depends upon \[{{p}^{th}}\]power of its mass m, \[{{q}^{th}}\]power of its velocity v and \[{{r}^{th}}\] power of Planck's constant h. Then the sum of values of \[p\], q and r is -K. Find the value of K7.
A)
2 done
clear
B)
4 done
clear
C)
5 done
clear
D)
1 done
clear
View Solution play_arrow
-
question_answer25)
The mass of a body is 20.000 g and its volume is 10.00 \[c{{m}^{3}}\]. If the measured values are expressed to the correct significant figures, find the maximum error in the value of density in \[(g\,c{{m}^{-3}})\].
A)
0.003 done
clear
B)
0.001 done
clear
C)
0.004 done
clear
D)
0.002 done
clear
View Solution play_arrow