Two bodies of mass $10 \ kg$ and $5 \ kg$ are moving in concentric circular orbits of radii $R$ and $r$ respectively such that their periods are same. The ratio between their centripetal acceleration is

Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles $\theta_1$ and $\theta_2$ respectively from the horizontal,then answer the following question. If $v_1 = v_2$ and $\theta_1 > \theta_2$,then choose the incorrect statement.

$A$ particle of mass $10\, g$ moves along a circle of radius $6.4\, cm$ with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8 \times 10^{-4}\, J$ by the end of the second revolution after the beginning of the motion? .............. $m/s^2$

The position vector of a particle moving in a plane is given by $r = a \cos \omega t \hat{i} + b \sin \omega t \hat{j}$, where $\hat{i}$ and $\hat{j}$ are the unit vectors along the rectangular axes $X$ and $Y$; $a$, $b$, and $\omega$ are constants, and $t$ is time. The acceleration of the particle is directed along the vector:

Twelve persons are initially at $12$ corners of a regular polygon of $12$ sides of side length $a$. Each person moves with a uniform speed $v$ in such a manner that person $1$ is always directed towards person $2$,person $2$ towards person $3$,person $3$ towards person $4$,and so on. The time after which they meet is

$A$ particle of mass $m$ moves along a circular path of constant radius $r$. The centripetal acceleration of the particle $a_c$ varies 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?