Two balls of different masses have the same kinetic energy. Then the

Options

A. heavier ball has greater momentum than the lighter ball
B. lighter ball has greater momentum than the heavier ball
C. both balls have equal momentum
D. both balls have zero momentum

Answer

A

Explanation

Let the two balls have same kinetic energy and their potential energy is zero. Therefore,
`(1)/(2) m_(1) v_(1)^(2) = (1)/(2) m_(2) v_(2)^(2) = k :. v_(1) = sqrt(( 2 k)/( m_(1))) and v_(2) = sqrt((2 k)/( m_(2)))`
`p _(1) = sqrt( 2 m_(1) k) and p_(2) = sqrt( 2 m_(2) k) `
`:. (p_(1))/( p_(2)) = sqrt((2 m_(1) k)/( 2 m_(2) k)) = sqrt((m_(1))/(m_(2))). Let m_(1) gt m_(2) , " then " sqrt(( m_(1))/( m_(2))) gt 1 `
`rArr p_(1) gt p_(2)`
So, the ball with greater mass will have greater momentum