Physics, asked by jaideepreddy8732, 9 months ago

A ball A moving with momentum 2ˆ 6 ˆ i j  collides with another identical moving ball B with momentum 4 ˆ  j and momentum of ball B after collision is 2 ˆj . The coefficient of restitution in the collision is 15 x . Find the value of x.

Answers

Answered by abhi178
0

Given info : A ball A moving with momentum 2i + 6j collides with another identical moving ball B with momentum 4 j and momentum of ball B after collision is 2 j.

To find : the coefficient of restitution is 15x then find the value of x.

solution : balls are identical means masses are equal. Let mass of each ball is m.

initial velocity of ball A = (2i + 6j)/m

[ momentum/mass = velocity as you know it ]

initial velocity of ball B = 4j/m

final velocity of ball B = 2j/m

from law of conservation of linear momentum,

initial momentum = final momentum

⇒(2i + 6j) + 4j = P + 2j

⇒2i + 8j = P

so, final velocity of ball A = (2i + 8j)/m

Now coefficient of restitution = relative velocity after collision/relative velocity before collision.

= |(2i + 8j - 2j)/m|/|(2i + 6j - 4j)/m|

= |2i + 6j|/|2i + 2j|

= √40/√8

= √5

given , coefficient of restitution is 15x

so, 15x = √5

⇒x = 1/3√5

Therefore the value of x is 1/3√5

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