Units and Measurements · Question 7

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 ]

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are :

1. Personal errors
2. Least count errors
3. Random errors
4. Instrumental errors

A metal wire has mass (0.4 0.002) g, radius (0.3 0.001) mm and length (5 0.02) cm. The maximum possible percentage error in the measurement of density will nearly be :

1. 1.3%
2. 1.6%
3. 1.4%
4. 1.2%

The dimensions [ MLT-2A-2] belong to the

1. Magnetic flux
2. Self inductance
3. Magnetic permeability
4. Electric permittivity

Plane angle and solid angle have

1. Units but no dimensions
2. Dimensions but no units
3. No units and no dimensions
4. Both units and dimensions