Units and Measurements · Question 28

A physical quantity of the dimensions of length that can be formed out of c, G and e24 0 is [c is velocity of light, G is the universal constant of gravitation and e is charge]

1. c2 [G e24 0 ]1/2
2. 1c2 [ e2G 4 0 ]1/2
3. 1cG e24 0
4. 1c2 [G e24 0 ]1/2

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length ?

1. hGc3/2
2. hGc5/2
3. hcG
4. Gch3/2

If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as [ x y rz] where , and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by

1. -1, -1, -1
2. 1, 1, 1
3. 1, -1, -1
4. -1, -1, 1

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be

1. [EV-2T-2]
2. [E-2V-1T-3]
3. [EV-2T-1]
4. [EV-1T-2]

If force (F), velocity (V) and time (T) are taken as fundamental units, then dimensions of mass are

1. [FVT-1]
2. [FVT-2]
3. [FV-1T-1]
4. [FV-1T]

In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows P = a3 b2cd. % error in P is

1. 7%
2. 4%
3. 14%
4. 10%

The pair of quantities having same dimensions is

1. Impulse and Surface Tension
2. Angular momentum and Work
3. Work and Torque
4. Young's modulus and Energy

The dimensions of ( 0 0)-1/2 are

1. [ L1/2T-1/2]
2. [ L-1T]
3. [ LT-1]
4. [ L1/2T1/2]

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

1. kg m s-1
2. kg m s-2
3. kg s-1
4. kg s

The density of a material in CGS system of units is 4 g cm-3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be

1. 0.04
2. 0.4
3. 40
4. 400