A $2 \mathrm{kg}$ block is gently pushed from rest at $\mathrm{A}$ and it slides down along the fixed smooth circular surface. If the attached spring has a force constant $\mathrm{k}=20 \mathrm{N} {\mathrm{m}}^{-1}$, then what is the unstretched length of the spring so that it does not allow the block to leave the surface until the angle with the vertical is $\mathrm{\theta }={60}^{°}$?

A car moves at a constant speed on a road as shown in the figure. The normal force by the road on the car are $N_{\mathrm{A}}$ and $N_{\mathrm{B}}$ when it is at the points $\mathrm{A}$ and $\mathrm{B}$, respectively. Then

A section of a fixed smooth circular track of radius $R$ in vertical plane is shown in the figure. A block is released from the position $A$ and leaves the track at $B$. The radius of curvature of its trajectory when it just leaves the track at $B$ is

A cube of mass $m$ starts at rest from point $1$ at a height $4R$, where $R$ is the radius of the circular track. The cube slides down the frictionless track and around the loop. The force which the track exerts on the cube at point $2$ is