Question
A ball of mass 3 kg moving with a velocity of 4 m/s undergoes a perfectly-elastic directcentral impact with a stationary ball of mass m. After the impact is over, the kinetic energy of the 3 kg ball is 6 J. The possible value(s) of m is/are
Options :
6 kg only
1 kg, 9 kg
1 kg only
1 kg, 6 kg
Answer :
1 kg, 9 kg
Solution :
Momentum is conserved
m1u1 + m2u2 = m1v1 + m2v2
3 × 4 + 0 = 3v1 + mv2 ...(i)
Coefficient of restitution (e = 1)
e =( v2-v1)/u2-u1 = 1
(v2-v1)/4 = 1
(v2-v1) = 4 m/s
KE of m1 after impact is 6 J
m1v1²/2 = 6 J
v1= √((6x2)/3) = ±2 m/s
From equation (ii),
For v1 = +2 m/s
v2 = 6 m/s
For v1 = –2 m/s
v2 = 2 m/s
From equation (i),
For v2 = 6 m/s
m = 1 kg
For v2 = 2 m/s
m = 9 kg
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