Units and Measurements

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

The dimension of 0 0 is equal to that of: ( 0 = Vacuum permeability and 0 = Vacuum permittivity)

1. Voltage
2. Inductance
3. Resistance
4. Capacitance

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

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

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of MP LQ TR AS, where value of 'Q' and 'R' are

1. (3, -5)
2. (-2, 1)
3. (-2, 2)
4. (1, -1)