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 aquires a max speed v and amax kinetic energy K. If instead the mass intially compresses the spring twice as far.

A- Its max speed will be 2v and it's max kenitic energy will be Sqroot(2) K.

B- Its max speed will be 4v and it's max kenitic energy will b 2 K.

C- Its max speed will be v Sqroot(2) and it's max kenitic energy will b 2 K.

D- Its max speed will be 2v and it's max kenitic energy will b 4 K.

E- Its max speed will be 2v and it's max kenitic energy will b 2 K.

Explanation / Answer

D- Its max speed will be 2v and it's max kenitic energy will b 4 K.

reason-

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

then,

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

as k and m cann't change,

when .

x doubles, v has to be doebled,

and hence K becomes 4 times

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