Units and Measurements · Question 7

L, C and R represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula M L2 T-4 A-2 corresponds to .

1. R LC
2. RLC
3. C LR
4. 1R LC

Match List-I with List-II. where h (Planck's constant), G (gravitational constant) and c (speed of light in vacuum) as fundamental units. Choose the correct answer from the options given below :

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

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A, respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA, respectively. The estimated error in the resistance measurement is .

1. 0.25
2. 2
3. 2.5
4. 0.18

In a screw gauge when the circular scale is given five complete rotations it moves linearly by 2.5 mm. If the circular scale has 100 divisions, the least count of screw gauge is mm.

1. 1 10-2
2. 1 10-3
3. 5 10-2
4. 5 10-3

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