Question

Which of the following quantities have unit as Newton-metre (N-m)?

(A) Work

(B) Energy

(C) Torque

(D) Power

(E) Momentum

Choose the correct answer from the options given below:

• A. (C) only
• B. (A), (B) and (C) only
• C. (B) only
• D. (D) and (E) only

Hint:

Think about which of these are scalar quantities that share the same unit as work, and which ones bring in time or velocity instead.

Answer 1

The Correct Option is B

We can also check each quantity using dimensional analysis instead of definitions.

Force has dimension $[MLT^{-2}]$ and distance has dimension $[L]$, so force times distance has dimension $[ML^2T^{-2}]$, matching the unit N.m.

Work equals force times distance, dimension $[ML^2T^{-2}]$, unit N.m. This fits.

Energy has the same dimension as work, $[ML^2T^{-2}]$, unit N.m. This fits too.

Torque equals force times perpendicular distance, dimension $[ML^2T^{-2}]$, unit N.m, even though it is kept apart from joule to reflect its vector nature. This also fits.

Power equals work divided by time, dimension $[ML^2T^{-3}]$, unit N.m/s, the watt. This does not reduce to N.m alone.

Momentum equals mass times velocity, dimension $[MLT^{-1}]$, unit kg.m/s. This has no match with N.m.

Only Work, Energy and Torque reduce to N.m, confirming the answer.

\[\boxed{\text{(A), (B) and (C) only}}\]