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QAIPMT-2010-Ph-2081: NEET 2010 Physics - Class 11 AIPMT-2010-Ph-2081 Solution: A ball moving with velocity 2 m/s collides head on with another …
A ball moving with velocity 2 m/s collides head on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in m/s) after collision will be
Multiple Choice Options
- A 0, 1
- B 1, 1
- C 1, 0.5
- D 0, 2
Step-by-Step Verified Solution
Here, m 1
= m, m 2
= 2m, u 1
= 2 m/s, u 2
= 0
Coefficient of restitution, e = 0.5
Let v 1
and v 2
be their respective velocities after
collision.
Applying the law of conservation of linear
momentum, we get
m 1 u 1
+ m 2 u 2
= m 1
v 1
+ m 2
v 2
_ m _ 2 + 2m _ 0 = m _ v 1
+ 2m _ v 2
or 2m = mv 1 + 2mv 2 or 2 = (v 1 + 2v 2 ) ...(i)
By definition of coefficient of restitution,
e = v 2 _ v 1 u 1 _ u 2
or e(u 1 � u 2 ) = v 2 � v 1 _ 0.5(2 �
0) = v 2 � v 1 ...(ii)
Solving equations (i) and (ii), we get
v 1 = 0 m/s, v 2 = 1 m/s