Units and Measurements

The potential energy of a particle changes with distance x from a fixed origin as V= A xx+B, where A and B are constants with appropriate dimensions. The dimensions of AB are .

1. [ M1L5/2T-2]
2. [ M3/2L5/2T-2]
3. [ M1L2T-2]
4. [ M1L7/2T-2]

The percentage error in the calculated volume of a sphere, if there is 2% error in its diameter measurement, is .

1. 1
2. 2
3. 6
4. 8

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

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

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and 7th Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has

1. 0.07 cm negative zero error
2. 0.7 cm negative zero error
3. 0.07 cm positive zero error
4. 0.7 cm positive zero error

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