(B) The centripetal acceleration is given by $a_c = k^2rt^2$. Since $a_c = \frac{v^2}{r}$,we have $\frac{v^2}{r} = k^2rt^2$. Solving for $v$,we get $v

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(B) The centripetal acceleration is given by $a_c = k^2rt^2$. Since $a_c = \frac{v^2}{r}$,we have $\frac{v^2}{r} = k^2rt^2$. Solving for $v$,we get $v^2 = k^2r^2t^2$,which implies $v = krt$. 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 $F_t$ responsible for the change in speed is $F_t = m a_t = mkr$. The power $P$ delivered to the particle is given by $P = F_t \cdot v$. Substituting the values,$P = (mkr) \cdot (krt) = mk^2r^2t$.

Class 11 Physics 3-2.Motion in Plane Kinematics Circular Motion (Uniform Angular Accelaration)

Difficult

$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as $a_c = k^2rt^2$,where $k$ is a constant. What is the power delivered to the particle by the force acting on it?

A
$2\pi mk^2r^2$
B
$mk^2r^2t$
C
$\frac{mk^4r^2t^5}{3}$
D
Zero

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3-2.Motion in Plane

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Kinematics Circular Motion (Uniform Angular Accelaration)

$A$ wheel rotates with a uniform angular acceleration of $2.0 \ rad/s^2$. If the wheel starts from rest,the number of revolutions completed in the first $10 \ s$ will be approximately:

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$A$ wheel is subjected to uniform angular acceleration about its axis. Initially,its angular velocity is zero. In the first $2 \ s$,it rotates through an angle ${\theta _1}$. In the next $2 \ s$,it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}/{\theta _1}$ is:

MediumAIIMS 1985

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$A$ wheel rotates with an angular acceleration of $3 \ rad \ s^{-2}$ and an initial angular velocity of $2 \ rad \ s^{-1}$. What will be its angular displacement after $2 \ s$?

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$A$ particle performing $U.C.M.$ of radius $\frac{\pi}{2} \ m$ makes $x$ revolutions in time $t$. Its tangential velocity is

DifficultMHT CET 2020

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$A$ ceiling fan starts from rest and makes $10$ revolutions in the first $3$ seconds. If the angular acceleration remains constant,how many revolutions will it make in the next $3$ seconds?

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$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as $a_c = k^2rt^2$,where $k$ is a constant. What is the power delivered to the particle by the force acting on it?

Similar Questions

$A$ wheel rotates with a uniform angular acceleration of $2.0 \ rad/s^2$. If the wheel starts from rest,the number of revolutions completed in the first $10 \ s$ will be approximately:

$A$ wheel is subjected to uniform angular acceleration about its axis. Initially,its angular velocity is zero. In the first $2 \ s$,it rotates through an angle ${\theta _1}$. In the next $2 \ s$,it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}/{\theta _1}$ is:

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