If the angular momentum of the body is increased by 50%, its rotational kinetic energy is increased by …………

Options

A. `125%`
B. `50%`
C. `100%`
D. `25%`

Answer

A

Explanation

`K=(L^(2))/(2I)` here 2I = constant
`therefore KalphaL^(2)`
`therefore (K_(2))/(K_(1))=((L_(2))/(L_(1)))^(2)` but 50% of `L_(2)+L_(1)`
`=L_(1)+0.5L_(1)`
`therefore (K_(2))/(K_(1))=((3)/(2))^(2)=(3)/(2)L_(1)`
`therefore (K_(2))/(K_(1))=(9)/(4)`
`therefore (K_(2)-K_(1))/(K_(1))xx100=(9-4)/(4)xx100%`
`therefore (K_(2)-K_(1))/(K_(1))xx100=(5)/(4)xx100=125%`