wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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

Open in App
Solution

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


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Rubbing It In: The Basics of Friction
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon