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A block of mass m moving at a speed v co...

A block of mass m moving at a speed v compresses a spring throgh a distance x before its speed is halved. Find the spring constant of the spring.

A

`(3 mv^2)/(4x^(2))`

B

`(mv^(2))/(4x^(2))`

C

`(mv^(2))/(2x^(2))`

D

`(2mv^(2))/(x^2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Applying conservation of energy, we get
`(1)/(2) mv^(2) = (1)/(2) m ((v)/(2))^(2) + (1)/(2) kx^(2)`
`rArr (1)/(2) kx^(2) = (mv^(2) )/(2) - (mv^(2))/(8) rArr kx^(2) = (3)/(4) mv^(2)`
`therefore k= (3 mv^(2) )/(4x^(2))`.
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