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A block of mass m moving with velocity v on a smooth horizontal surface hits the spring of constant k as shown.the max. compression in the spring is?

a) \sqrt{2m/k} .v
b) \sqrt{m/k} .v
c) \sqrt{m/2k} .v



The block has mass m
it is moving with kinetic energy 1/2mv²
it strikes the spring with speed v and comes to rest after moving distance x
so its kinetic energy must equal to spring Potential energy
 \frac{1}{2}mv^2= \frac{1}{2}kx^2 \\ x^2= \frac{m}{k}v^2 \\ x=v \sqrt{ \frac{m}{k} }
so its option b)
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