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A riding ball of mass m strikes a rigid ...

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

A

Mv

B

2mV

C

`(mV)/(2)`

D

`(mV)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `p_(i)=p_(f)=Mv`
Change in momentum of the ball=`bar(p)_(f)=bar(p)_(i)`
`=(-p_(f_(x))hati-p_(f_(y))hatj)-(p_(i_(x))hati-p_(i_(y))hatj)`
`=-hati(p_(f_(x))-p_(ix))-hatj(p_(f_(y))-p_(i_(y)))`
`=-2hatip_(ixhati)=-mVhati[therefore p_(f_(y))-p_(iy)=0]`
`"Here"p_(ix)-p_(fx)cos 60^(@)=(mV)/(2)`
Impulse imparted by the wall=Change in the momentum of the ball=mV
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