Question

The quantities which have the same dimensions as those of solid angle are :

• A. strain and angle
• B. stress and angle
• C. strain and arc
• D. angular speed and stress

Answer 1

The Correct Option is A

The problem asks us to identify quantities that share the same dimensions as those of a solid angle. A solid angle is a dimensionless quantity, meaning it has no physical dimensions (its dimensional formula is M⁰L⁰T⁰).

Now, let's evaluate each option:

• Strain and angle: Both strain and angle are dimensionless quantities. Strain is the ratio of change in dimension to original dimension, and angle is defined as the ratio of arc length to radius, both resulting in no units. Hence, they share the same dimensions as a solid angle.
• Stress and angle: Stress has dimensions of force per unit area, represented as M¹L^-1T^-2, which is not dimensionless.
• Strain and arc: While strain is dimensionless, an arc is a physical length measured in units, so it is not dimensionless.
• Angular speed and stress: Angular speed has dimensions of T^-1 while stress has M¹L^-1T^-2. Neither is dimensionless.

Thus, the correct answer is strain and angle, as both have the same dimensions as a solid angle.