A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k2 rt2, where k is a constant. The power delivered to the particle by the force acting on it is given as

mk2 r2 t

mk2 r2 t2

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Physics NCERT Exemplar Solutions Class 12th Chapter Eight Physics Class 11th Work, Energy and Power

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k² rt², where k is a constant. The power delivered to the particle by the force acting on it is given as

Option 1 -

zero

Option 2 -

mk² r² t²

Option 3 -

mk² r² t

Option 4 -

mk² rt

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1 Answer

Answered by

Raj Pandey | Contributor-Level 9

2 weeks ago

Correct Option - 3

Detailed Solution:

a = k2rt2

$\Rightarrow \frac{v^{2}}{r} = k^{2} r t^{2}$

$\Rightarrow v = k r t$

$a_{t} = \frac{d v}{d t} = k r$

? tangential force, F_t = ma_t = mkr

$∴ P o w e r d e l i v e r e d, P = F_{t} v = (m k r) (k r t) = m k^{2} r^{2} t$

Note ® Power delivered by centripetal force will be zero.

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