Units and Measurements

The time period of a simple harmonic oscillator is T = 2 mk. Measured value of mass (m) of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant (k) is %.

1. 3.43
2. 7.60
3. 3.35
4. 6.76

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

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

In an experiment, a set of readings are obtained as follows: 1.24 mm, 1.25 mm, 1.23 mm, 1.21 mm. The expected least count of the instrument used in recording these readings is mm.

1. 0.01
2. 0.05
3. 0.001
4. 0.1

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

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

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%