JEE Main202528 Jan 2025Morning ShiftPhysicsWork, Power and EnergyActual
A bead of mass ' m ' slides without friction on the wall of a vertical circular hoop of radius ' R ' as shown in figure. The bead moves under the combined action of gravity and a massless spring ( k ) attached to the bottom of the hoop. The equilibrium length of the spring is ' R '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes '
Options
- A3 Rg + kR ^2 ~m
- B2 gR + kR ^2 ~m
- C2 Rg + kR ^2 ~m
- D2 Rg + 4 kR ^2 ~m
Correct answer
A. 3 Rg + kR ^2 ~m
Step-by-step solution
aligned Work done by gravity & =m g (2 R-R 60^ ) & = 3 m g R 2 aligned aligned Work done by spring & =- 1 2 k (0^2-R^2 ) & = 1 2 k R^2 aligned Net work = change in kinetic energy i.e. 3 m g R 2 + k R^2 2 = 1 2 m v^2 or v^2=3 g R+ k R^2 m or v= 3 g R+ k R^2 m