Units and Measurements

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of -0.004 cm, the correct diameter of the ball is

1. 0.521 cm
2. 0.525 cm
3. 0.053 cm
4. 0.529 cm

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