A particle is moving with uniform speed along the circumference of a circle of radius $R$ under the action of a central fictitious force $F$ which is inversely proportional to $R ^{3}$. Its time period of revolution will be given by
$T \propto R ^{2}$
$T \propto R ^{\frac{3}{2}}$
$T \propto R ^{\frac{5}{2}}$
$T \propto R ^{\frac{4}{3}}$
A particle moves with constant angular velocity in a circle. During the motion its
A stone tied to the end of a string of $1\, m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolution in $44\, seconds$, what is the magnitude and direction of acceleration of the stone?
Two particles, one at the centre of a circle of radius $R$, and another at a point $Q$ on the circle, start moving towards a point $P$ on the circle at the same time (see figure below). Both are at rest initially and move with uniform velocities $\vec{V}_1$ and $\overrightarrow{V_2}$ respectively. They also reach the point $P$ at the same time, If the angle between the velocities is $\theta$ and the angle subtended by $P$ and $Q$ at the centre is $\phi$ (as shown in the figure), then
A particle is tied to $20\, cm$ long string. It performs circular motion in vertical plane. What is the angular speed of particle when the tension in the string at the top is zero ......... $rad/sec$
If a particle is moving on a circular path with constant speed, then the angle between the direction of acceleration and its position vector w.r.t. centre of circle will be ............