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The momentum of a body increases by 50% ...

The momentum of a body increases by 50% due to change in its velocity. The kinetic energy of the body increases by

A

`125% `

B

`50% `

C

`250% `

D

`sqrt(50)% `

Text Solution

Verified by Experts

The correct Answer is:
A
Let original momentum `p_1 = 100 alpha`
Final momentum = `150 alpha`
`(p_1^2)/(p_2^2) = (2mk_1)/(2mk_2) = (k_1)/(k_2)`
`((100 alpha)/(150 alpha))^2 = (k_1)/(k_2)`
`therefore (2/3)^2 = (k_1)/(k_2) implies 4/9 = (k_1)/(k_2)`
`therefore k_2 = (9k_1)/(4)`
`therefore` Percentage increament in `k = ("Change in KE")/("Original KE") xx 100`
`= (k_2 - k_1)/(k_1) xx 100`
`= (9/4 k_1 - k_1)/(k_1) xx 100 = 5/4 xx 100 = 125%`
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