The kinetic energy of a body becomes four times its intial value , the new linear momentum will be `………..`

Options

A. four times the initial value
B. three times the initial value
C. twice the initial value
D. same as initial value

Answer

C

Explanation

If P is momentum and K is the kinetic energy .
`K = (p^(2))/(2m)` when m = mass of body
` :. (p^(2))/K =2m ` constant
` :. (p_(1)^(2))/(K_(1))=(p_(2)^(2))/(K_(2))`
But `K_(2) =4K_(1)`
` :. (p_(1)^(2))/(p_(2)^(2)) =(K_(1))/(4K_(2))`
But ` ((p_(1))/(p_(2)))^(2) =1/4`
` :. (p_(1))/(p_(2))= 1/2 `
` :. p_(2) = 2p_(1)`