A smooth curved surface of height $$10m$$ is ended horizontally. A spring of force constant $$200$$ $$Nm-1$$ is fixed at the horizontal end as shown in figure. When an object of mass $$10$$ g is released from the top, it travels along the curved path and collides with the spring. Then, the maximum compression in the spring is (Take$$, $$g=10$$ $$ms-2)

Question

A smooth curved surface of height $$10m$$ is ended horizontally. A spring of force constant $$200$$ $$Nm-1$$ is fixed at the horizontal end as shown in figure. When an object of mass $$10$$ g is released from the top, it travels along the curved path and collides with the spring. Then, the maximum compression in the spring is (Take$$, $$g=10$$ $$ms-2)

Infinity Learn · Accepted Answer

Let the maximum compression in the spring be x. From law of conservation of energy, $$mgh$$$$=12kx2$$              $$10$$×$$10-3$$×$$10$$×$$10=12$$×$$200$$×$$x2$$⇒                                     $$x2=10$$×$$10-3=10-2$$⇒                                     $$x=1100=110m=0.1mThus$$, compression in the spring is $$0.1m$$.

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