A collar $B$ of mass $2 \mathrm{kg}$ is constrained to move along a horizontal smooth and fixed circular track of radius $5 \mathrm{m}$. The spring lying in the plane of the circular track and having spring constant $200 \mathrm{N} {\mathrm{m}}^{-1}$ is undeformed when the collar is at $A$. If the collar starts from rest at $B$, the normal reaction exerted by the track on the collar when it passes through $A$ is

A mass $m$ starting from $A$ reaches $B$ of a frictionless track. On reaching $B$, it pushes the track with a force equal to $x$ times its weight, then the applicable relation is

Figure shows a smooth vertical circular track $AB$ of radius $R$. A block slides along the surface $AB$ when it is given a velocity equal to $\sqrt{6gR}$ at point $A$. The ratio of the force exerted by the track on the block at point $A$ to that at point $B$ is:

A bead of mass $m$ is released from rest at $A$ to move along the fixed smooth circular track as shown in the figure. The ratio of magnitudes of centripetal force and normal reaction by the track on the bead at any point $P_0$ described by the angle $\theta \left(\ne 0\right)$ would

Two bodies of masses $m$ and $4m$ are attached to a light string as shown in figure. A body of mass $m$ hanging from string is executing oscillations with angular amplitude $60°$, while other body is at rest on a horizontal surface. The minimum coefficient of friction between mass $4m$ and the horizontal surface is (here pulley is light and smooth)

Ball $A$ of mass $m$, after sliding from an inclined plane, strikes elastically another ball $B$ of same mass at rest. Find the minimum height $h$ so that ball $B$ just completes the circular motion of the surface at $C$. (All surfaces are smooth.)

Two particles describe the same circle of radius $R$ in the same direction with the same speed $v$, then at the given instant relative angular velocity of $2$ with respect to $1$ will be

A block $m$ slides down a curved frictionless track, starting from rest. The curve obeys the equation $y=\frac{x^2}{2}$. The tangential acceleration of the block is