Units and Measurements

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%