Momentum and CollisionMedium
Question
A ball moving with velocity 2 m/s collides head on with another stationary ball of doubled the mass. If the coeffient of restitution is 0.5, then their velocities (in m/s) after collision will be
Options
A.0, 1
B.1, 1
C.1, 0.5
D.0, 2
Solution
Here, m1 = m, m2 = 2m
u1 = 2m/s, u2 = 0
Let v1 and v2 be their respectiv velocities after collision.
Applying the law of consevation of linear momentum, we get
m1u1 + m2u2 = m1u1 + m2u2
∴ m × 2 + m × 0 = m × v1 + 2m × v2
or, 2m = mv1 + 2mv2
or, 2 = (v1 + 2v2) .......(i)
By definations of coefficient of restitution,
or, e(u1 - u2) = v2 - v1
0.5(2 - 0) = v2 - v1 .......(ii)
1 = v2 - v2
Solving equation (i) and (ii), we get
v1 = 0 v1 = 0m/s, v2 = 1 m/s.
u1 = 2m/s, u2 = 0
Let v1 and v2 be their respectiv velocities after collision.
Applying the law of consevation of linear momentum, we get
m1u1 + m2u2 = m1u1 + m2u2
∴ m × 2 + m × 0 = m × v1 + 2m × v2
or, 2m = mv1 + 2mv2
or, 2 = (v1 + 2v2) .......(i)
By definations of coefficient of restitution,
or, e(u1 - u2) = v2 - v1
0.5(2 - 0) = v2 - v1 .......(ii)
1 = v2 - v2
Solving equation (i) and (ii), we get
v1 = 0 v1 = 0m/s, v2 = 1 m/s.
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