Þ a = 1/2
Now putting a = 1/2 in equation (3)
Þ 
Þ b = 3/2
On substituting value a, b and c in equation (1) T = k(d)1/2 (r)3/2 (s)_1/2
Þ 
Hence the correct answer is (c).
Level-3
Illustration 1. A spherical body of mass m and radius r is allowed to fall in a medium of viscosity h. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v) is called time constant (t). Dimensionally t can be represented by (5 min)
(a)
(b) 
(c) 
(d) None of these
Solution.
The dimensional formulae of mass = [M]
The dimensional formulae of radius = [L]
The dimensional formulae of viscosity = M1L_1T1
So lets check the dimensions of each option
The dimension of 
is 
therefore option (a) is not correct.
The dimensions of 
is 
therefore option (b) is also not correct.
The dimension of 
is 
therefore option (c) is also not correct.
Hence the correct answer is (d).
Illustration 2. The damping force for a body moving through a fluid is proportional to velocity. What will be the dimensional formula for the constant of proportionality ? (3 min)
(a) MLT_1 (b) ML0T_1
Þ a = 1/2
Now putting a = 1/2 in equation (3)
Þ
Þ b = 3/2
On substituting value a, b and c in equation (1) T = k(d)1/2 (r)3/2 (s)_1/2
Þ
Hence the correct answer is (c).
Level-3
Illustration 1. A spherical body of mass m and radius r is allowed to fall in a medium of viscosity h. The time in which the velocity of the body increases from zero to 0.63 times the terminal velocity (v) is called time constant (t). Dimensionally t can be represented by (5 min)
(a) (b)
(c) (d) None of these
Solution.
The dimensional formulae of mass = [M]
The dimensional formulae of radius = [L]
The dimensional formulae of viscosity = M1L_1T1
So lets check the dimensions of each option
The dimension of is therefore option (a) is not correct.
The dimensions of is therefore option (b) is also not correct.
The dimension of is therefore option (c) is also not correct.
Hence the correct answer is (d).
Illustration 2. The damping force for a body moving through a fluid is proportional to velocity. What will be the dimensional formula for the constant of proportionality ? (3 min)
(a) MLT_1 (b) ML0T_1