Units and Measurements · Question 5

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 ]

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%