Physics Work & Energy DUHS 2022
PMDC Verified Question 57 of 108
The rate of doing work is zero, when the angle \( \theta \) between force and velocity is:
A
\( \theta = 60^{\circ} \)
B
\( \theta = 180^{\circ} \)
C
\( \theta = 0^{\circ} \)
D
\( \theta = 90^{\circ} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \( \theta = 90^{\circ} \)
Concept:

The rate of doing work is Power, which can be expressed as the dot product of the Force and Velocity vectors.

Formula:

$$ P = \vec{F} \cdot \vec{v} = Fv \cos \theta $$

Solution:

  • For power to be zero while force and velocity are non-zero, the cosine term must be zero.


  • \( \cos \theta = 0 \implies \theta = 90^{\circ} \).


  • When force is perpendicular to velocity (like centripetal force), no work is done, hence the rate of work is zero.


Why other options are incorrect:

At 0°, rate is maximum. At 180°, rate is maximum negative (rapid deceleration). At 60°, it is exactly half of the maximum.

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