A mass is pressed against (but is not attached to) an ideal horizontal spring on

Question

A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed v and a maximum kinetic energy K. If instead the mass initially compresses the spring twice as far: (a) Its maximum speed will be 2v and its maximum kinetic energy will be 2K. (b) Its maximum speed will be 2v and its maximum kinetic energy will be ?2K. (c) Its maximum speed will be ?2v and its maximum kinetic energy will be 2K. (d) Its maximum speed will be 4v and its maximum kinetic energy will be 2K. (e) Its maximum speed will be 2v and its maximum kinetic energy will be 4K.

Explanation / Answer

Correct answer is option (E): Its max speed will be 2v and it's max kenitic energy will b 4 K

let when max displacemnt is x, speed is v and energy K,

then,

1/ kx^2 = 1/2mv^2

as k and m can't change,

when x doubles, v has to be double,

and hence K becomes 4 times

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