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A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is

Asked in JEE Main 9th Jan 1st Shift 2019 · Energy stored and maximum compression

• (1) F/(√mk)
• (2) F/(π√mk)
• (3) (π F)/(√mk)
• (4) (2F)/(√mk)

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives a π here; dividing by π looks like a period being confused with a speed, but the maximum speed follows from energy balance alone.
• (3) No single slip gives a π here; a factor from the period 2π√m/k has crept into what is a pure energy balance.
• (4) Comes from ignoring the spring's stored energy and using the full amplitude 2F/k in 1/2mv²=Fx.

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