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 :

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 n2 R t2 where n is a constant. The power delivered to the particle by the force acting on it, is : (A) M n2 R2 t (B) M n R2 t (C) M n R2 t2 (D) (1/2) M n2 R2 t2

Tardigrade Admin · Accepted Answer

(V2/R)=n2 R t2 ⇒ V2=n2 R2 t2 ⇒ V=n R t ⇒ (d V/d t)=n R P=Ft V =(m d V/d t) V =m n R .n R t P=n2 R2 t m

Q. 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 :

$M n^{2} R^{2} t$

$M n R^{2} t$

$M n R^{2} t^{2}$

$\frac{1}{2} M n^{2} R^{2} t^{2}$

$\frac{V ^{2}}{R} = n^{2} R t^{2}$
$\Rightarrow V^{2} = n^{2} R^{2} t^{2}$
$\Rightarrow V = n Rt$
$\Rightarrow \frac{d V}{d t} = n R$
$P = F_{t} V$
$= \frac{m d V}{d t} V$
$= mn R . n Rt$
$P = n^{2} R^{2} t m$

Q. 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 n2Rt2 where n is a constant. The power delivered to the particle by the force acting on it, is :

Mn2R2t

MnR2t

MnR2t2

21​Mn2R2t2