Units and Measurements

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]

A screw gauge gives the following readings when used to measure the diameter of a wire Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is :

1. 0.052 cm
2. 0.52 cm
3. 0.026 cm
4. 0.26 cm