Units and Measurements · Question 3

Consider that s, kB, b represents Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of s kB-1 b is

1. [ L-1T-1K-4]
2. [ L-1T-1K-2]
3. [ L-1K-2]
4. [ L-1T-1K-3]

One main scale division of a Vernier calliper is equal to 1 mm and the number of divisions on the Vernier scale is 10. When both the jaws touch each other, the Vernier scale shifts to the left of zero of the main scale in such a way that 4th Vernier division coincides with a division of the main scale. If this Vernier calliper measures the length of the wire to be 1 cm, the actual length of the wire is :

1. 1.04 cm
2. 0.60 cm
3. 0.96 cm
4. 1.00 cm

A physical quantity P is related to four observations a, b, c and d as follows: P = a3b2/c d The percentage errors of measurement in a, b, c and d are 1\%, 3\%, 2\%, and 4\% respectively. The percentage error in the quantity P is

1. 13\%
2. 15\%
3. 10\%
4. 2\%

Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and the zero of V.S. is at x = 0.1 cm when the jaws of Vernier callipers are closed. If the main scale reading for the diameter is M = 5 cm and the number of coinciding vernier division is 8, the measured diameter after zero error correction, is

1. 4.98 cm
2. 5.00 cm
3. 5.18 cm
4. 5.08 cm

In a vernier callipers, (N+1) divisions of vernier scale coincide with N divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:

1. 110N
2. 1100(N+1)
3. 100N
4. 10(N+1)

The quantities which have the same dimensions as those of solid angle are:

1. strain and angle
2. stress and angle
3. strain and arc
4. angular speed and stress

A force defined by F = t2 + t acts on a particle at a given time t. The factor which is dimensionless, if and are constants, is:

1. t/
2. t/
3. t
4. /t

In an electrical circuit, the voltage is measured as V = (200 4) volt and the current is measured as I = (20 0.2) A. The value of the resistance is:

1. (10 4.2)
2. (10 0.3)
3. (10 0.1)
4. (10 0.8)

The pitch of an error free screw gauge is 1 mm and there are 100 divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads 1 mm and 63rd division on the circular scale coincides with the reference line. The diameter of the wire is:

1. 1.63 cm
2. 0.163 cm
3. 0.163 m
4. 1.63 m

The potential energy of a particle moving along x-direction varies as V = Ax2 x + B. The dimensions of A2B are:

1. [ M3/2 L1/2 T-3 ]
2. [ M1/2LT-3 ]
3. [ M2L1/2T-4 ]
4. [ ML2 T-4 ]