Question

A particle performing uniform circular motion has angular momentum `L`. When its angular velocity is doubled and `K.E` is also doubled, the new angualr momentum becomes `x` times. What is `x` ?

Answer 1

Correct Answer - `(1)`
Here, `L_(1) = I_(1) omega_(1)`, When `omega_(2) = 2 omega_(1)`,
and `KE = (1)/(2)I_(2)omega_(2)^(2) = 2 ((1)/(2)I_(1)omega_(1)^(2))`
`(1)/(2)I_(2) (2omega_(1))^(2) = 2 xx (1)/(2)I_(1)omega_(1)^(2) , I_(2) = (1)/(2)I_(1)`
`:. L_(2) = I_(2)omega_(2) = (1)/(2)I_(1) xx 2omega_(1) = I_(1)omega_(1) = L_(1)`
`x = (L_(2))/(L_(1)) = 1`