A ball A hits balls B and C placed symmetrically simultaneously. The mass of ball A is m , the mass of B is 2 m , and that of C is m . After hitting, A comes to rest, and B and C fly off, making an an

Question

A ball A hits balls B and C placed symmetrically simultaneously. The mass of ball A is $m$ , the mass of B is $2 m$ , and that of C is $m$ . After hitting, A comes to rest, and B and C fly off, making an angle of $6 0^{\circ}$ between them.

Let the coefficient of restitution between A and B be $e_{1}$ and that between A and C be $e_{2}$ . Then the $(1/10)^{t h}$ value of the percentage loss in kinetic energy during collision is...

TestHub · Accepted Answer

Let I 2 ​ ​ and I 3 ​ ​ be the impulse on B and C, respectively, during the collision. So, the change in momentum of A is − ( I 2 ​ ​ + I 3 ​ ​ ) . Thus, m V = I 2 ​ ​ + I 3 ​ ​ . sin 12 0 ∘ m V ​ 3 ​ m V ​ 3 ​ mV ​ V 2 ​ K in ​ ( K f ​ ) b ​ ( K f ​ ) c ​ K f ​ K f ​ K E ​ ( % l oss ) K E ​ /10 ​ = sin 3 0 ∘ I 2 ​ ​ = sin 3 0 ∘ I 3 ​ ​ = I 2 ​ = I 3 ​ = 2 m V 2 ​ = m V 3 ​ = 2 3 ​ V ​ an d V 3 ​ = 3 ​ V ​ = 2 1 ​ m V 2 = 2 1 ​ × 2 m × ( 2 3 ​ ) 2 V 2 ​ = 3 1 ​ 4 m V 2 ​ = 2 1 ​ m 3 V 2 ​ = 3 1 ​ ( 2 m V 2 ​ ) = 12 m V 2 ​ [ 2 + 1 ] = 4 m V 2 ​ = K in ​ K in ​ − K f ​ ​ = 2 m V 2 ​ 2 m V 2 ​ − 4 m V 2 ​ ​ × 100% = 50% = 5 ​

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JEE Advanced 2027 (Class 12+)

JEE Main 2027 (Class 12)