A 1 kg ball moving with speed of 10 m/s collides
head on with a 2 kg ball moving in opposite
direction with speed of 20 m/s. If collision is
perfectly inelastic the speed of the balls will be
(1) 10 m/s
(2) 20 m/s
(3) 15 m/s
(4) 5 m/s
Answers
Answer:
a
Explanation:
inelastic only linear momentum could be conserved hence assuming after collision they travell together then v=10m/s
Answer: a)10m/s
Speed of the balls is -10m/s and loss in kinetic energy is 300J
Explanation:
Given: Mass of ball = 1kg
Speed of moving ball = 10m/s
Mass of 2nd ball = 2kg
Speed of 2nd ball = 20m/s
Let initial velocities of 1kg ball and 2kg ball be u1,u2 respectively and final velocities be v1,v2 respectively .
By conservation of linear momentum ,
1 × u1 + 2 × u2 = 1 × v1 + 2 × v2
u1 = 10m/s and u2 = -20m/s.
v1 + 2v2 = -30m/s ..... (i)
Coefficient of restitution e = 0 (As the collision is perfectly inelastic)
e = (v2 - v1)/(u2 - u1)
∵ e =0
v2 - v1 = 0
v2 = v1
Putting v2 = v1 in equation (i) we get:-
v2 = -10m/s
Similarly, v1 = -10m/s
Loss of kinetic energy, ΔK.E = 1/2[ u1² + 2u2² - v1² - v2²]
ΔK.E = 1/2[ 100 + 800 - 100 - 200]
ΔK.E = 1/2[ 600]
ΔK.E = 300J
Hence, the speed of the balls is 10m/s and loss in kinetic energy is 300J
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