Units and Measurements

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

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

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

A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is

1. e2 - e1
2. e1 + 2e2
3. e1 + e2
4. e1 - 2e2

The dimension of 12 0 E2, where 0 is permittivity of free space and E is electric field, is

1. ML2T-2
2. ML-1T-2
3. ML2T-1
4. MLT-1

If the dimensions of a physical quantity are given by MaLbTc, then the physical quantity will be

1. velocity if a = 1, b = 0, c = -1
2. acceleration if a = 1, b = 1, c = -2
3. force if a = 0, b = -1, c = -2
4. pressure if a = 1, b = -1, c = -2

If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be

1. 8%
2. 2%
3. 4%
4. 6%

Which two of the following five physical parameters have the same dimensions ? 1. Energy density 2. Refractive index 3. Dielectric constant 4. Young's modulus 5. Magnetic field

1. 1 and 4
2. 1 and 5
3. 2 and 4
4. 3 and 5

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be

1. [ML2T-2]
2. [ML2T-1I-1]
3. [ML2T-3I-2]
4. [ML2T-3I-1]

The velocity v of a particle at time t is given by v = at + bt+c, where a, b and c are constants. The dimensions of a, b and c are

1. [L], [LT] and [LT-2]
2. [LT-2], [L] and [T]
3. [L2], [T] and [LT-2]
4. [LT-2], [LT] and [L]

The ratio of the dimensions of Planck's constant and that of moment of inertia is the dimensions of

1. time
2. frequency
3. angular momentum
4. velocity

The dimensions of universal gravitational constant are

1. [ M-1L3T-2]
2. [ ML2T-1]
3. [ M-2L3T-2]
4. [ M-2L2T-1]

The dimensions of Planck's constant are equal to those of

1. energy
2. momentum
3. angular momentum
4. power

Which pair does not have equal dimensions?

1. Energy and torque
2. Force and impulse
3. Angular momentum and Planck constant
4. Elastic modulus and pressure