Dimensional Analysis

Q.

The frequency $f$ of vibration of mass m suspended from a spring of spring constant k is given by$f=c{m}^x{k}^y$where $c$ is a dimensionless constant. The values of $x$ and $y$ are respectively

1. $\frac{1}{2},\frac{1}{2}$

2. $-\frac{1}{2},\frac{1}{2}$

3. $\frac{1}{2},-\frac{1}{2}$

4. $-\frac{1}{2},-\frac{1}{2}$

Q.

Force of viscosity acting on a spherical body of radius $r$ moving with velocity $v$ through a fluid of viscosity is given by

Q. Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful

1. $\frac{A}{B}$
2. $A+B$
3. can be A and B
4. $A-B$

Q.

Find out the dimensions of the constants a and b in the Vander Waal's equation $[p+\frac{a}{v^2}](V-b)=RT$

where p is pressure, v is volume, R is gas constant and T is temperature.

$\begin{array}{cc}Column-I& Column-II\\ a& \left(i\right)\left[M{L}^5{T}^{-2}\right]\\ b& \left(ii\right)\left[M^2{L}^3{T}^{-1}\right]\\ & \left(iii\right)\left[M^0{L}^3{T}^0\right]\\ & \left(iv\right)\left[M^0{L}^2{T}^{-1}\right]\end{array}$

1. a - (iv); b - (ii)

2. a - (ii); b - (iv)

3. a - (iii); b - (i)

4. a - (i); b - (iii)

Q. What happen if any particle moves with the speed of light ? The mass of particle will increase or decrease ?

Q.

A quantity is given by $f=\surd (h{c}^5/G)$, where $c$ is speed of light, $G$ is universal gravitational constant and $h$ is the Planck’s constant. Dimension of $f$ is that of;

1. Area

2. Energy

3. Volume

4. Momentum

Q. A radioactive source emits three types of radiation.
a) Name the radiation which travels with the speed of light.
b) Name the radiation which has the highest ionising power.
c) Name the radiation consisting of the same kind of particles as the cathode rays.

Q. The unit of $\frac{L}{R}$ is (where L= inductance and R= resistance)

1. $se{c}^{-1}$
2. volt
3. sec
4. Ampere

Q. The velocity of a particle depends upon as v = a + bt + $c{t}^2$ ; if the velocity is in m/sec, the unit of a will be

1. $m/se{c}^2$
2. $m/sec$
3. $m^2/sec$
4. $m/se{c}^3$

Q. Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful?

1. $\frac{A}{B}$
2. A+B
3. A-B
4. None

Q. Dimensions of $\frac{1}{{\mu }_0{ϵ}_0}$ , where symbols have their usual meaning are :

1. $L^{-1}T$
2. ${LT}^{-1}T$
3. $L^2{T}^{-2}$
4. $L^2{T}^2$

Q. The ratio of SI to cgs units of force is

1. ${10}^{-5}$
2. ${10}^5$
3. ${10}^{-3}$
4. ${10}^3$

Q. If the units of velocity of light '$C$', Gravitational constant '$G$' and Planck's Constant '$h$' are taken as fundamental units, the dimensional formula for Mass in the new system will be :

1. $\left[C^1{G}^1{h}^1\right]$
2. $\left[C^{\frac{1}{2}}{G}^{\frac{1}{2}}{h}^{\frac{1}{2}}\right]$
3. $\left[C^2{G}^2{h}^2\right]$
4. $\left[C^{\frac{1}{2}}{G}^{-\frac{1}{2}}{h}^{\frac{1}{2}}\right]$

Q. Young's modulus of a material has the same units as

1. Pressure
2. Strain
3. Compressibility
4. Force

Q. Define 1 dioptre of power of a lens.

Q. Definition for coulambs law and superposition law?

Q. A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12cm below the surface, the radius of this circle in cm is: A) 36 5 B) 4 5 C) 36 7 D) 36/7

Q. If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimension of gravitational constant is

1. $c^2{g}^0{p}^{-2}$
2. $c^0{g}^2{p}^{-1}$
3. $c{g}^3{p}^{-2}$
4. $c^{-1}{g}^0{p}^{-1}$

Q. A motor of 100 H.P. moves a load with a uniform speed of 72 km/hr. The forward thrust applied by the engine on the car is

1. 1111 N
2. 3550 N
3. 3730 N
4. 2222 N

Q. $kg.m/s^2$ is the unit of

1. Force
2. Momentum
3. Acceleration
4. Velocity

Q.

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 $g=4{\pi }^2\left(\frac{l}{T^2}\right)$ will be

1. 2%

2. 4%

3. 7%

4. 10%

Q. If P represents radiation pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, then non-zero integers x, y and z such that $P^x{Q}^y{C}^z$ is dimensionless, are

1. x=1, y=1, z=-1
2. x=1, y=-1, z=1
3. x=-1, y=1, z=1
4. x=1, y=1, z=1

Q. If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then the dimensions of mass in new system is

1. $c^{\frac{1}{2}}{G}^{\frac{1}{2}}{h}^{\frac{1}{2}}$
2. $c^{\frac{1}{2}}{G}^{\frac{1}{2}}{h}^{\frac{-1}{2}}$
3. $c^{\frac{1}{2}}{G}^{\frac{-1}{2}}{h}^{\frac{1}{2}}$
4. $c^{\frac{-1}{2}}{G}^{\frac{1}{2}}{h}^{\frac{1}{2}}$