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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

1.25

B

0.5

C

2.5

D

`sqrt(50%)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let original momentum `p_(1)=100alpha`,
Final momentum=150`alpha`
`(p_(1)^(2))/(p_(2)^(2))=(2mk_(1))/(2mk_(2))=(k_(1))/(k_(2))`
`((100alpha)/(150alpha))^(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")xx100`
`=(k_(2)-k_(1))/(k_(1))xx100`
`=((9)/(4)k_(1)-k_(1))/(k_(1))xx100=(5)/(4)xx100=125%`
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