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  • 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 n2 R t2 where n i

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 n2 R t2 where n is a constant.  The power delivered to the particle by the force acting on it, is

Option: 1

 M n2 R2 t


Option: 2

M n R2 t


Option: 3

 M n R2 t2

 


Option: 4

\frac{1}{2}  M n2 R2 t2

 


Answers (1)

best_answer

\\ \text{ Centripetal acceleration}, a_{c}=n^{2} r t^{2} where, a_{c}=\frac{v^{2}}{r} \\ \\ \Rightarrow \frac{v^{2}}{r}=n^{2} r t^{2} \Rightarrow v=n r t \dots(1) \\ \text{tangential acceleration}, a_{t}=\frac{d v}{d t}=n r \dots(2) \\ \\ \text{Tangential force acting on the particle}, F=M a_{t}=Mn r \\ \\ \text{Power delivered}, P=\vec{F} \cdot \vec{v}=F v \cos \theta \\ \\ \therefore P=F v=(Mn r) \times n r t\left(\because \theta=0^{\circ}\right) \Longrightarrow P=M n^{2} r^{2} t

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Ritika Harsh

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