Units and Measurements · Question 20

In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division = 0.05 mm, then the least count of the vernier callipers is mm.

1. 0.002
2. 0.02
3. 0.05
4. 0.005

In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is mm. [Assume least count is 0.01 mm]

1. 1.54
2. 1.50
3. 1.51
4. 1.48

Four persons measure the length of a rod as 20.00 cm, 19.75 cm, 17.01 cm and 18.25 cm. The relative error in the measurement of average length of the rod is :

1. 0.18
2. 0.24
3. 0.06
4. 0.08

A ball of radius r and density dropped through a viscous liquid of density and viscosity attains its terminal velocity at time t, given by t = A a rb c d, where A is a constant and a, b, c and d are integers. The value of b + ca + d is .

Match the LIST-I with LIST-II Choose the correct answer from the options given below:

1. A-III, B-II, C-IV, D-I
2. A-I, B-IV, C-II, D-III
3. A-II, B-I, C-IV, D-III
4. A-II, B-IV, C-I, D-III

In an experiment the values of two spring constants were measured as k1 = (10 0.2) N/m and k2 = (20 0.3) N/m. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

1. 1.33%
2. 2.67%
3. 1.67%
4. 2.33%

Consider a modified Bernoulli equation. (P + ABt2 ) + g(h + Bt) + 12 V2 = constant If t has the dimension of time then the dimensions of A and B are , respectively.

1. [ ML0T-1] and [M0LT]
2. [ ML0T-2] and [ M0LT-1]
3. [ ML0T-2] and [ M0LT-2]
4. [ ML0T-1] and [ M0LT-1]

A spherical body of radius r and density falls freely through a viscous liquid having density and viscosity and attains a terminal velocity v0. Estimated maximum error in the quantity is : (Ignore errors associated with , and g, gravitational acceleration)

1. 2 [ rr - v0v0 ]
2. 2 [ rr + v0v0 ]
3. 2 rr + v0v0
4. 2 rr - v0v0

Keeping the significant figures in view, the sum of the physical quantities 52.01 m, 153.2 m and 0.123 m is :

1. 205.3 m
2. 205 m
3. 205.333 m
4. 205.33 m

A quantity Q is formulated as X-2Y+ 32Z- 25. X, Y, and Z are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of Q is

1. 0.6
2. 0.8
3. 0.7
4. 0.1