Units and Measurements

The equation of stationary wave is : y=2a ( 2 ) ( 2 x ). Which of the following is NOT correct :

1. The dimensions of nt is [L]
2. The dimensions of n is [ LT-1]
3. The dimensions of x is [L]
4. The dimensions of n/ is [T]

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\%

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

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

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