Question 167: Work, Energy and Power & Circular Motion

Question

A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n
2
R t
2
where n is a constant. The power delivered to the particle by the force acting on it, is :

Accepted Answer

We know,
centripetal acceleration = $${{{V^2}} \over R}$$
$$ 	herefore $$   According to question,
$${{{V^2}} \over R}$$ = $${n^2}R{t^2}$$
$$ \Rightarrow $$   V
2
= n
2
R
2
t
2
$$ \Rightarrow $$   V = nRt
$$ \Rightarrow $$   $${{dV} \over {dt}}$$ = nR
Power (P) = Force (F) $$ 	imes $$ Velocity (V)
= M $${{dV} \over {dt}}$$(V)
= M (nR) (nRt)
= Mn
2
R
2
t

Answer

M n
2
R
2
t

Answer

M n R
2
t

Answer

M n R
2
t
2

Answer

$${1 \over 2}$$ M n
2
R
2
t
2

Work, Energy and Power & Circular Motion

A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n 2 R t 2 where n is a constant. The power delivered to the particle by the force acting on it, is :

Choose the correct answer: