(B) Given centripetal acceleration $a_c = k^2 r t^2$.We know that $a_c = \frac{v^2}{r}$,where $v$ is the speed of the particle.Equating the two expres

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(B) Given centripetal acceleration $a_c = k^2 r t^2$.We know that $a_c = \frac{v^2}{r}$,where $v$ is the speed of the particle.Equating the two expressions: $\frac{v^2}{r} = k^2 r t^2$.This simplifies to $v^2 = k^2 r^2 t^2$,so $v = krt$.The tangential acceleration $a_t$ is given by $a_t = \frac{dv}{dt} = \frac{d}{dt}(krt) = kr$.The tangential force acting on the particle is $F_t = m a_t = mkr$.The power $P$ delivered to the particle is the product of the tangential force and the velocity: $P = F_t \cdot v = (mkr) \cdot (krt) = m k^2 r^2 t$.

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

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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 $a_c = k^2 r t^2$. The power delivered to the particle by the forces acting on it is:

IIT 1994 All IIT

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

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3-2.Motion in Plane

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Kinematics Circular Motion (Uniform Angular Accelaration)

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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 $a_c = k^2 r t^2$. The power delivered to the particle by the forces acting on it is:

Similar Questions

$A$ 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 $2 \ s$?

$A$ car is moving at a speed of $72 \, km/h$. The diameter of its wheels is $0.25 \, m$. If the wheels stop after completing $20$ revolutions upon applying brakes,the angular retardation produced by the brakes is ....... $rad/s^2$. (in $.5$)

$A$ wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first $2 \text{ s}$ it rotates through an angle $\theta_1$ and in the next $2 \text{ s}$ it rotates through an angle $\theta_2$. The ratio $\frac{\theta_2}{\theta_1}$ is . . . . . . .

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