BITSAT2024PhysicsWork, Power and EnergyActual
An ideal massless spring S can be compressed 1 m by a force of 100 N in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane inclined at 30^ to the horizontal. A 10 kg block M is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring by 2 m . If g=10 ~m / s ^2 , what is the speed of mass just before it touches the spring?
Options
- A20 ~m / s
- B30 ~m / s
- C10 ~m / s
- D40 ~m / s
Correct answer
A. 20 ~m / s
Step-by-step solution
F=k x k= F x = 100 1 ~N / m =100 ~N / m Now, from energy conservation, between natural length of spring and its maximum compression state. 1 2 m v^2+m g h= 1 2 k x_ ^2 aligned v & = k x_ ^2 m -2 g h & = (100)(2)^2 10 -(2)(10) ( 2 2 ) = 20 ~m / s aligned