Units and Measurements

A new unit ( ) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of units if light takes 6 min. 40 s to cover this distance?

1. 200
2. 400
3. 300
4. 500

Consider the equation H= xp qErts Where H = magnetic field intensity; E = electric field, = permittivity, x = distance, t = time The values of p, q, r and s respectively are :

1. 1, 1, 1, 1
2. -1, 1, 2, 1
3. 1, -1, -2, 1
4. -1, -2, -2, 1

The density of a uniform cylinder is determined by measuring its mass m, length l and diameter d. The measured values of m, l and d are 97.42 0.02 g, 8.35 0.05 mm and 20.20 0.02 mm, respectively. Calculated percentage fractional error in is .

1. 0.63%
2. 0.82%
3. 0.72%
4. 0.25%

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

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

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