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A block of mass m is initially moving to...

A block of mass m is initially moving to the right on a horizontal frictionless surface at a speed v. It then compresses a spring of spring constant k. At the instant when the kinetic energy of the block is equal to the potential energy of the spring, the spring is compressed a distance of :

A

`vsqrt(m //2k)`

B

`vsqrt(m //k)`

C

`vsqrt(m //4k)`

D

`mv^2//4k`

Text Solution

Verified by Experts

The correct Answer is:
A
Initially, total energy `= 1/2 m v^2`
At the given instant, `P.E = K.E = 1/2 T.E. implies P.E. = 1/4 mv^2 implies 1/2 kx^2 = 1/4 mv^2 implies x = v sqrt(m/(2k))`.
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