Units and Measurements

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