Question 98: Work, Energy and Power & Circular Motion

Question

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 = k
2
rt
2
, where k is a constant. The power delivered to the particle by the force acting on it is given as

Accepted Answer

$${a_r} = {k^2}r{t^2} = {{{v^2}} \over r}$$
$$ \Rightarrow {v^2} = {k^2}{r^2}{t^2}$$ or $$v = krt$$
and $${{d|v|} \over {dt}} = kr$$
$$ \Rightarrow {a_t} = kr$$
$$ \Rightarrow |\overline F \,.\,\overline v | = (mkr)(krt)$$
$$ = m{k^2}{r^2}t = $$ power delivered

Answer

zero

Answer

mk
2
r
2
t
2

Answer

mk
2
r
2
t

Answer

mk
2
rt

Work, Energy and Power & Circular Motion

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 = k 2 rt 2 , where k is a constant. The power delivered to the particle by the force acting on it is given as

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