Units and Measurements

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]