(B) The centripetal acceleration is given by $a_c = \frac{v^2}{R} = n^2 R t^2$.From this,the square of the velocity is $v^2 = n^2 R^2 t^2$,which impli

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(B) The centripetal acceleration is given by $a_c = \frac{v^2}{R} = n^2 R t^2$.From this,the square of the velocity is $v^2 = n^2 R^2 t^2$,which implies $v = nRt$.The tangential acceleration is $a_t = \frac{dv}{dt} = \frac{d}{dt}(nRt) = nR$.The power delivered to the particle is $P = F_t v = (M a_t) v$.Substituting the values,$P = M(nR)(nRt) = M n^2 R^2 t$.

Class 11 Physics 3-2.Motion in Plane Mix Examples-Motion in Plane

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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 $n^2Rt^2$ where $n$ is a constant. The power delivered to the particle by the force acting on it,is

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A
$\frac{1}{2} M n^2 R^2 t^2$
B
$M n^2 R^2 t$
C
$M n R^2 t^2$
D
$M n R^2 t$

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Mix Examples-Motion in Plane

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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 $n^2Rt^2$ where $n$ is a constant. The power delivered to the particle by the force acting on it,is

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$A$ particle has initial velocity $(2\hat{i} + 3\hat{j})$ and acceleration $(0.3\hat{i} + 0.2\hat{j})$. The magnitude of velocity after $10\, s$ will be:

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Two particles $A$ and $B$ start at the origin $O$ and travel in opposite directions along a circular path of radius $0.5\,m$ at constant speeds $0.5\,m/s$ and $1.5\,m/s$,respectively. The time when they collide with each other is ........ $\text{s}$.

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