A bead of mass 'm' is attached to one end of a spring of natural length R & spring constant `k = ((sqrt3 + 1))/(R)`. The other end of the spring is fixed at point A on a smooth vertical ring of radius R as shown. The normal reaction at B just after it is released to move is

A bead of mass m is attached to one end of a spring of natural length R and spring constant K=((sqrt(3)+1)mg)/(R ) . The other end of the spring is fixed at a point A on a smooth vertical ring of radius R as shown in fig. The normal reaction at B just after it is released to move is

A Bead of mass m is attached to one end of a spring of natural length 'R' and spring cosntant 'k=((sqrt3+1)mg)/R' . The other end of the spring is fixed at point 'A' on a smooth vertical ring of radius 'R' as shown

A block of mass 'm' is attached to a spring in natural length of spring constant 'k' . The other end A of the spring is moved with a constat velocity v away from the block . Find the maximum extension in the spring.

A ring of mass m is attached to a horizontal spring of spring constant k and natural length l_0 . The other end of the spring is fixed and the ring can slide on a horizontal rod as shown. Now the ring is shifted to position B and released Find the speed of the ring when the spring attains its natural length.

A bead of mass m can slide without friction on a fixed circular horizontal ring of radius 3R having a centre at the point C. The bead is attached to one of the ends of spring of spring constant k. Natural length of spring is R and the other end of the spring is R and the other end of the spring is fixed at point O as shown in the figure. If the bead is released from position A, then the kinetic energy of the bead when it reaches point B is

A block of mass m is attached to one end of a mass less spring of spring constant k. the other end of spring is fixed to a wall the block can move on a horizontal rough surface. The coefficient of friction between the block and the surface is mu then the compession of the spring for which maximum extension of the spring becomes half of maximum compression is .

A solid sphere of radius R and density rho is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3rho . The complete arrangement is placed in a liquid of density 2rho and is allowed to reach equilibrium. The correct statements(s) is (are)

A ball of mass m is attached to the lower end of a light vertical spring of force constant K . The upper end of the spring is fixed. The ball is released from rest with the spring at its normal ( unstretched ) length, and comed to rest again after descending through a distance x .

A small block of mass m, can move without friction on the outside of a fixed vertical circular track of radiusR. The block is attached to a spring of natural length R//2 and spring constant K. The other end of spring is connected to a point at height R//2 directly above the centre of track. If the block is released from rest when the spring is in horizontal state (see figure) then at that moment,

A small block of mass m, can move without friction on the outside of a fixed vertical circular track of radiusR. The block is attached to a spring of natural length R//2 and spring constant K. The other end of spring is connected to a point at height R//2 directly above the centre of track. If the complete stup is in a gravity free space, then the minimum speed (v_(0)) required at the highest point A to just reach the lowest point is