If the angular momentum of a rotating body about a fixed axis is increased by 10%. Its kinetic energy will be increased by

Options

A. 0.1
B. 0.2
C. 0.21
D. 0.05

Answer

C

Explanation

Kinetic energy of rotation , `K_(R) = (L^(2))/(2I)`
For a given I (moment of inertia of a body) , `K_(R) prop L^(2)`
When the angular momentum of a body is increased by 10% i.e., `(L)/(10)` , its angular momentum will become
`L. = L + (L)/(10) = (11L)/(10)`
`therefore (K._(R))/(K_(R)) = (L.^(2))/(L^(2)) = (((11L)/(10))^(2))/(L^(2)) = (121)/(100) , or K._(R) = (121)/(100) K_(R)`
Percentage increase in the kinetic energy
`(K._(R) - K_(R))/(K_(R)) xx 100 % = ((121)/(100) K_(R) - K_(R))/(K_(R)) xx 100 % = 21 %`