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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA particle of mass \( m \) moves in a circular path of radius \( r \) in the \( x\text{--}y \) plane about the \( z \)-axis. A force \( \mathbf{F} \) acts on it such that its tangential component is \( F_t = F_0 \cos\theta \), where \( \theta \) is the angular displacement from \( \theta = 0 \). The work done by this force as the particle moves from \( \theta = 0 \) to \( \theta = \pi/2 \) is:
Correct answer · Option 2
\( F_0 r \)
Explanation
\( \tau = F_t r = F_0 r \cos\theta \). Work done \( W = \int_0^{\pi/2} \tau d\theta = F_0 r \int_0^{\pi/2} \cos\theta d\theta = F_0 r [\sin\theta]_0^{\pi/2} = F_0 r \).
