A rigid ball of mass m strikes a rigid wall at `60^@` and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be

Options

A. `mV`
B. `2mV`
C. `(mV)/(2)`
D. `(mV)/(3)`

Answer

A

Explanation

Given `p_i = p_f = mV `
change in momentum of the ball
` = vecp_f - vecp_i`
` = (- p_(fx ) hati -p_(fy) hatj) - (p_(ix ) hati - p_(iy) hatj )`
` =- hati (p_( fx )+p_(ix)) - hatj (p_(fy) 0p_(iy))`
`=- hati (p_(fx) =- mVhati [ :. p_(fy) - P_(iy)=0]`
here `,P_(ix) = P_(fx ) = P_(i ) cos 60^@ = (mV )/(2)`
` :. ` Impulse imparted by the wall = change in teh momentum of the ball = mV