In the figure shown there is a smooth tube of radius 'R' fixed in the vertical plane A ball 'B' of mass 'm'is released from the top of the tube B slides down due to gravity and compresses the spring the end 'C' of the spring is fixed and the end A is free Initially the line OA makes an angle of `60^(@)` with OC and finally it makes an angle of `30^(@)` after compression find the spring constant of the spring

In the figure shown, there is a smooth tube of radius R , fixed in the vertical plane. A ball B of mass m is released from the top of the tube. B slides down due to gravity and compresses the spring is fixed and end A is free., Initially, line OA makes an angle 60^@ with OC and finally it makes an angle of 30^@ after compression. Find the spring constant of the spring.

In the figure shown, there is a smooth tube of radius R , fixed in the vertical plane. A ball B of mass m is released from the top of the tube. B slides down due to gravity and compresses the spring is fixed and end A is free., Initially, line OA makes an angle 60^@ with OC and finally it makes an angle of 30^@ after compression. Find the spring constant of the spring.

In the figure shown, a small ball of mass 'm' can move witgout sliding in a fixed semicircular track of radius R in vertical planet. It is released from the top. The resultant force on the ball at the lowest of the track is

In the figure shown, a small ball of mass 'm' can move witgout sliding in a fixed semicircular track of radius R in vertical planet. It is released from the top. The resultant force on the ball at the lowest of the track is

A block of mass m is released from the top of fixed inclined smooth plane. if theta is the angle of inclination then vertical accelertion of block is

In the figure shown one end of a light spring of natural length l_(0)=sqrt(5/8)m(~~0.8m) is fixed at point D and other end is attached to the centre B of a uniform rod AF of length l_(0)//sqrt(3) and mass 10kg. The rod is free to rotate in a vertical plane about a fixed horizontal axis passing through the end A of the rod. The rod is held at rest in horizontal position and the spring is in relaxed state. It is found that, when the rod is released to move it makes an angle of 60^(@) with the horizontal when it comes to rest for the first time. Find the (a) the maximum elogation in the spring . (Approximately) (b) the spring constant. (Approximately)

In the figure shown one end of a light spring of natural length l_(0)=sqrt(5/8)m(~~0.8m) is fixed at point D and other end is attached to the centre B of a uniform rod AF of length l_(0)//sqrt(3) and mass 10kg. The rod is free to rotate in a vertical plane about a fixed horizontal axis passing through the end A of the rod. The rod is held at rest in horizontal position and the spring is in relaxed state. It is found that, when the rod is released to move it makes an angle of 60^(@) with the horizontal when it comes to rest for the first time. Find the (a) the maximum elogation in the spring . (Approximately) (b) the spring constant. (Approximately)

A smooth semicircular wire track of radius R if fixed in a vertical plane. One end of massless spring of netural length (3R)/(4) is attached to the lowest point O of the wire track. A small ring of mass m which can slide on the track is attched to the other end of the spring. the ring is held stationary at point P such that the spring makes an angle of 60^(@) with the vertical. The spring constant is K = (mg)/(R ) . considering the instance when the ring is released, the free body diagram of the ring, when a_(T) is tengential acceleration, F is restoring force and N is normal reaction is