Units and Measurements

The least count of a screw gauge is 0.01 mm. If the pitch is increased by 75% and number of divisions on the circular scale is reduced by 50%, the new least count will be 10-3 mm.

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation

1. E2=pc2+m2c4
2. E2=pc2+m2c2
3. E2=p2c2+m2c4
4. E2=p2c2+m2c2

The position of a particle moving on x-axis is given by x(t)=A t+B 2t+Ct2+D, where t is time. The dimension of ABCD is

1. L
2. L3 T-2
3. L2 T-2
4. L2

The electric flux is = + where and are linear and surface charge density, respectively. ( ) represents

1. displacement
2. charge
3. electric field
4. area

The energy of a system is given as E(t)= 3e- t, where t is the time and =0.3 s-1. The errors in the measurement of and t are 1.2\% and 1.6\%, respectively. At t=5 s, maximum percentage error in the energy is :

1. 6\%
2. 11.6\%
3. 4\%
4. 8.4\%

Match 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)-(III), (D)-(IV)
4. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)

If B is magnetic field and 0 is permeability of free space, then the dimensions of (B/ 0) is

1. MT-2A-1
2. L-1A
3. ML2T-2A-1
4. LT-2A-1

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

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

Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge respectively.

1. [F]= [ C M-1L-2T2 ]
2. [F]= [ C2M-2L2T2 ]
3. [F]= [ C2M-1L-2T2 ]
4. [F]= [ C M-2L-2T-2 ]

The maximum percentage error in the measurement of density of a wire is [Given, mass of wire =(0.60 0.003) g radius of wire =(0.50 0.01) cm length of wire =(10.00 0.05) cm]

1. 7
2. 8
3. 5
4. 4