For a body moving in a circular path, a condition for no skidding if $\mu $ is the coefficient of friction, is
$\frac{{m{v^2}}}{r} \le \mu mg$
$\frac{{m{v^2}}}{r} \ge \mu mg$
$\frac{v}{r} = \mu g$
$\frac{{m{v^2}}}{r} = \mu mg$
A particle at a distance of $1 m$ from the origin starts moving, such that $d r / d \theta=r$, where $r$ and $\theta$ are polar co-ordinates. Then, the angle between resultant velocity and tangential velocity is
A bob is whirled in a horizontal plane by means of a string with an initial speed of $\omega \mathrm{rpm}$. The tension in the string is $T$. If speed becomes $2 \omega$ while keeping the same radius, the tension in the string becomes:
A ball of mass $0.1$ kg is suspended by a string. It is displaced through an angle of ${60^o}$ and left. When the ball passes through the mean position, the tension in the string is ........ $N$
A car is travelling with linear velocity $v$ on a circular road of radius $r$. If it is increasing its speed at the rate of $'a'$ $meter/{\sec ^2}$, then the resultant acceleration will be
If the string of a conical pendulum makes an angle $\theta$ with horizontal, then square of its time period is proportional to