Units and Measurements

The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the Earth from the Sun, the distance between the Sun and the Earth in new unit is :

1. 3 108
2. 500
3. 3 1010
4. 400

In a vernier callipers, 20 VSD coincide with 16 MSD (each division of length 1 mm). The least count of the vernier callipers is :

1. 0.2 cm
2. 0.1 cm
3. 0.02 cm
4. 0.01 cm

Each side of a metallic cube of mass 5.580 kg is measured to be 9.0 cm. Keeping the significant figures in view, the density of the material of the cube can be best expressed as X 103 kg m-3, where the value of X is :

1. 7.654
2. 7.7
3. 7.65
4. 7.6

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