Units and Measurements

Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.

1. T2 = 4 2 rGM2
2. T2 = 4 2 r3
3. T2 = 4 2 r3GM
4. T2 = 4 2 r2GM

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

1. 511
2. 1011
3. 5011
4. 12

The dimensional formula of angular impulse is :

1. [ ML2T-2]
2. [ ML-2T-1]
3. [ ML2T-1]
4. [ MLT-1]

The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as r=(0.35 0.05) cm R=(100 10) ohm l=(15 0.2) cm The percentage error in resistivity of the material of the wire is :

1. 37.3\%
2. 25.6\%
3. 35.6\%
4. 39.9\%

If the percentage errors in measuring the length and the diameter of a wire are 0.1\% each. The percentage error in measuring its resistance will be:

1. 0.144%
2. 0.2%
3. 0.1%
4. 0.3%

A force is represented by F=ax2+bt 12 where x= distance and t= time. The dimensions of b2/a are:

1. [ ML2 T-3 ]
2. [ ML3 T-3 ]
3. [ MLT-2 ]
4. [ ML-1T-1 ]

Consider two physical quantities A and B related to each other as E= B-x2At where E, x and t have dimensions of energy, length and time respectively. The dimension of AB is

1. L-2M1T0
2. L2M-1T1
3. L0M-1T1
4. L-2M-1T1

The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is:

1. 6
2. 5
3. 4
4. 8

If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is 0.5 mm, the Vernier constant of traveling microscope is

1. 0.01 mm
2. 0.01 cm
3. 0.1 mm
4. 0.1 cm

If mass is written as m=kcPG-1/2h1/2 then the value of P will be : (Constants have their usual meaning with k a dimensionless constant)

1. 1/3
2. -1/3
3. 1/2
4. 2

The resistance R= VI where V=(200 5) V and I=(20 0.2) A, the percentage error in the measurement of R is :

1. 5.5%
2. 3%
3. 7%
4. 3.5%

A physical quantity Q is found to depend on quantities a, b, c by the relation Q= a4b3c2. The percentage error in a, b and c are 3\%, 4\% and 5\% respectively. Then, the percentage error in Q is :

1. 43%
2. 34%
3. 66%
4. 14%

Identify the physical quantity that cannot be measured using spherometer :

1. Radius of curvature of concave surface
2. Specific rotation of liquids
3. Thickness of thin plates
4. Radius of curvature of convex surface

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

1. Statement I is true but Statement II is false
2. Both Statement I and Statement II are false
3. Both Statement I and Statement II are true
4. Statement I is false but Statement II is true

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the correct answer from the options given below :

1. Both (A) and (R) are correct and (R) is the correct explanation of (A)
2. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
3. (A) is true but (R) is false
4. (A) is false but (R) is true

The equation of state of a real gas is given by (P+ aV2 )(V-b)=RT, where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of ab2 is similar to that of :

1. P
2. RT
3. PV
4. R