$A$ particle is moving in a circle of radius $R$ with constant speed $v$. If the radius is doubled while keeping the speed the same,what happens to the centripetal force?

In non-uniform circular motion,the ratio of tangential to radial acceleration is ($r=$ radius,$\alpha=$ angular acceleration,$V=$ linear velocity).

$A$ point object moves along an arc of a circle of radius $R$. Its velocity depends upon the distance covered $s$ as $v=K \sqrt{s}$,where $K$ is a constant. If $\theta$ is the angle between the total acceleration and tangential acceleration,then

In a circular motion of a particle,the tangential acceleration of the particle is given by $a_t = 12 \ m/s^2$. The radius of the circle is $3 \ m$. The particle was initially at rest. The time after which the total acceleration of the particle makes an angle $45^{\circ}$ with the radial acceleration is

$A$ particle is moving in a circular path of radius $r$ under the action of a force $F$. If at an instant the velocity of the particle is $\vec{v}$,and the speed of the particle is increasing,then:

$A$ particle moves along an arc of a circle of radius $R$. Its velocity depends on the distance covered as $v = a\sqrt{s}$,where $a$ is a constant. Then the angle $\alpha$ between the vector of the total acceleration and the vector of velocity as a function of $s$ will be: