Units and Measurements · Question 11

The dimensional formula of 12 0 E2 ( 0 = permittivity of vacuum and E = electric field) is MaLbTc. The value of 2a-b+c= .

1. 0
2. 1
3. -1
4. 2

The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured by a micrometer of least count 0.001 cm. The error in the measured Young's modulus is 109 N/m2. The value of is . (Ignore the contribution of the load to Young's modulus error calculation)

1. 1.3
2. 1.65
3. 0.13
4. 0.25

Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are .

1. [ hTLM-2 ]
2. [ hT-1LM-2 ]
3. [ hTL2M-2 ]
4. [ h-1T-1LM-2 ]

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are 100 divisions in circular scale and pitch of screw gauge is 0.1 mm. When diameter of a sphere is measured, the reading of main scale is 5 mm and 50th division of circular scale coincides with the reference line of main scale. The diameter of sphere is mm.

1. 5.045
2. 5.055
3. 5.450
4. 5.550

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, 4th mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and 5th division of vernier scale coincides with a main scale division. Measured length of cylinder is mm. (Least count of Vernier calliper = 0.1 mm)

1. 15.5
2. 15.4
3. 15.9
4. 15.1

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