$A$ motorcycle is moving on an overbridge of radius $R$. The driver maintains a constant speed $v$. As the motorcycle is ascending on the overbridge,the normal force on it is

$A$ stone of mass $2 \,kg$ is tied at one end of a string of length $2 \,m$ and is whirled in a horizontal circle. If the string can withstand a maximum tension of $64 \,N$, then the permissible maximum number of rotations per minute is

$A$ particle describes a horizontal circle of radius $r$ in a conical funnel with a smooth inner surface with a speed of $v = 0.5 \text{ m/s}$. The height $h$ of the plane of the circle from the vertex of the funnel is (acceleration due to gravity, $g = 10 \text{ m/s}^2$): (in $\text{ cm}$)

$A$ particle moves with constant angular velocity in a circular path of a certain radius and is acted upon by a certain centripetal force $F$. If the angular velocity is doubled,keeping the radius the same,the new force will be

$A$ simple pendulum has a length of $2 \,m$ and a bob of mass $100 \,g$. It is whirled in a horizontal plane. If the string breaks under a tension of $10 \,N$, what is the angle made by the string with the vertical? $\left(g=10 \,m/s^{2}\right)$

$A$ motorcycle driver doubles their velocity when taking a turn. The force exerted outwardly will be