Which of the following two quantities have the same dimensions?

Question

Accepted Answer

Step-by-step analysis:

1) Work and torque
- Work: force × displacement → dimensions $[M L T^{-2}]	imes[L]=[M L^{2} T^{-2}]$.
- Torque (moment of force): force × lever arm → same product → $[M L^{2} T^{-2}]$.
- Therefore they have the same dimensions.

2) Power and moment of inertia
- Power: energy/time → $[M L^{2} T^{-3}]$.
- Moment of inertia: mass × length² → $[M L^{2}]$.
- Not the same.

3) Work and angular displacement
- Angular displacement is dimensionless (radian) → $[1]$, while work is $[M L^{2} T^{-2}]$.
- Not the same.

4) Power and radius of circular motion
- Radius: $[L]$, power: $[M L^{2} T^{-3}]$.
- Not the same.

Only option (1) is correct.

FINAL_ANSWER: a

Answer

Answer

Answer