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

Step 1: Analyze the Dimensions of Solid Angle 

A solid angle is a dimensionless quantity as it is defined as the ratio of the area subtended on a sphere to the square of its radius:

$$ \Omega = \frac{\text{Area}}{\text{Radius}^2} $$

Step 2: Compare with Strain and Angle

Strain: Strain is also dimensionless, as it is defined as the ratio of change in length to the original length.

Angle: An angle is dimensionless, defined as the ratio of arc length to radius.

Step 3: Conclusion

Both strain and angle have the same dimensions as a solid angle.