(C) The centripetal acceleration is given by $a = \frac{v^{2}}{r}$.Given $a = k^{2} r t^{2}$,we have $\frac{v^{2}}{r} = k^{2} r t^{2}$.Solving for vel

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(C) The centripetal acceleration is given by $a = \frac{v^{2}}{r}$.Given $a = k^{2} r t^{2}$,we have $\frac{v^{2}}{r} = k^{2} r t^{2}$.Solving for velocity $v$,we get $v^{2} = k^{2} r^{2} t^{2}$,so $v = krt$.The tangential acceleration $a_{t}$ is the rate of change of speed: $a_{t} = \frac{dv}{dt} = \frac{d}{dt}(krt) = kr$.The tangential force $F_{t}$ is $m a_{t} = mkr$.The power $P$ delivered by the force is $P = \vec{F} \cdot \vec{v} = F_{t} v$.Substituting the values,$P = (mkr)(krt) = m k^{2} r^{2} t$.

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 circular path of constant radius $r$ such that its centripetal acceleration $a$ varies with time $t$ as $a = k^{2} r t^{2}$,where $k$ is a constant. The power delivered to the particle by the force acting on it is given as:

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$zero$
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$m k^{2} r^{2} t^{2}$
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$m k^{2} r^{2} t$
D
$m k^{2} r t$

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Mix Examples-Motion in Plane

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$A$ body $P$ is projected at an angle of $30^{\circ}$ with the horizontal and another body $Q$ is projected at an angle of $30^{\circ}$ with the vertical. If the ratio of the horizontal ranges of the bodies $P$ and $Q$ is $1: 2$, then the ratio of the maximum heights reached by the bodies $P$ and $Q$ is

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$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a$ varies with time $t$ as $a = k^{2} r t^{2}$,where $k$ is a constant. The power delivered to the particle by the force acting on it is given as:

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Four bodies $P, Q, R$ and $S$ are projected with equal velocities having angles of projection $15^{\circ}, 30^{\circ}, 45^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The body having the shortest range is

Two projectiles are fired from the ground with the same initial speeds from the same point at angles $(45^{\circ}+\alpha)$ and $(45^{\circ}-\alpha)$ with the horizontal direction. The ratio of their times of flight is

The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $h_m$. Here $h_m$ as a function of $\phi$ can be represented as:

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