Units and Measurements

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

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

The equation for real gas is given by (P + aV2 )(V - b) = RT, where P, V, T and R are the pressure, volume, temperature and gas constant, respectively. The dimension of ab-2 is equivalent to that of :

1. Compressibility
2. Planck's constant
3. Energy density
4. Strain

If 0 and 0 are the permeability and permittivity of free space, respectively, then the dimension of ( 1 0 0 ) is :

1. T2/L
2. L2/T2
3. T2/L2
4. L/T2

Given a charge q, current I and permeability of vacuum 0. Which of the following quantity has the dimension of momentum ?

1. qI/ 0
2. q2 0 I
3. q 0/I
4. q 0 I

The pair of physical quantities not having the same dimensions is :

1. Angular momentum and Planck's constant
2. Torque and energy
3. Surface tension and impulse
4. Pressure and Young's modulus

The expression given below shows the variation of velocity (v) with time (t), v = At2 + BtC + t. The dimension of ABC is :

1. [ M0L1T-2]
2. [ M0L2T-3]
3. [ M0L2T-2]
4. [ M0L1T-3]

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

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

A physical quantity Q is related to four observables a, b, c, d as follows : Q= ab4cd where, a=(60 3) Pa; b=(20 0.1) m; c=(40 0.2) N s m-2 and d=(50 0.1) m, then the percentage error in Q is x1000, where x= .

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of [MaLbTc]. If b = -3, the value of c is .

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be x100 where x is .