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Center of Mass and Collision question

2016 · Q143
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Center of Mass and Collision question

2016 · Q143

NEETPhysicsCenter of Mass and CollisionMCQ+4 / −1
A rigid ball of mass m strikes a rigid wall at 60o 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 :
NEET 2016 Phase 2 Physics - Center of Mass and Collision Question 34 English
  1. A
    mVmVmV
  2. B
    2 mVmVmV
  3. C
    mV2{{mV} \over 2}2mV​
  4. D
    mV3{{mV} \over 3}3mV​
View written solutionFree

Correct answer: A

NEET 2016 Phase 2 Physics - Center of Mass and Collision Question 34 English Explanation

Given, pi = pf = mV
Change in momentum of the ball

=p→f−p→i = {\overrightarrow p _f} - {\overrightarrow p _i}=p​f​−p​i​

=(−pfxi^−pfyj^)−(−pixi^−piyj^) = \left( { - {p_{fx}}\widehat i - {p_{fy}}\widehat j} \right) - \left( { - {p_{ix}}\widehat i - {p_{iy}}\widehat j} \right)=(−pfx​i−pfy​j​)−(−pix​i−piy​j​)

=−i^(pfx+pix)−j^(pfy+piy) = - \widehat i\left( {{p_{fx}} + {p_{ix}}} \right) - \widehat j\left( {{p_{fy}} + {p_{iy}}} \right)=−i(pfx​+pix​)−j​(pfy​+piy​)

=−2pixi^=−mVi^[∵pfy−piy=0] = - 2{p_{ix}}\widehat i = - mV\widehat i\left[ \because {{p_{fy}} - {p_{iy}} = 0} \right]=−2pix​i=−mVi[∵pfy​−piy​=0]

Here, pix = pfx = picos 60° = mV2{{mV} \over 2}2mV​

∵\because∵ Impulse imparted by the wall = change in the momentum of the ball = mV.

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