Units and Measurements

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

The area of a rectangular field (in m2) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is

1. 138 101
2. 1382
3. 1382.5
4. 14 102

The physical quantity that has the same dimensional formula as pressure is

1. Coefficient of viscosity
2. Force
3. Momentum
4. Young's modulus of elasticity

The percentage error in the measurement of g is : (Given that g = 4 2 LT2, L = (10 0.1) cm, T = (100 1) s)

1. 7%
2. 2%
3. 5%
4. 3%

If E and G respectively denote energy and gravitational constant, then EG has the dimensions of :

1. [M2] [L-2] [T-1]
2. [M2] [L-1] [T0]
3. [M] [L-1] [T-1]
4. [M] [L0] [T0]