Question

two masses m and 2m are placed in a fixed horizontal circular smooth hollow tube of radius R as shown the mass m is moving with speed U and the mass 2 m is stationary after the first collision the time elapsed for next collision (coefficient of restitution= 1/ 2)

Answer 1

Explanation:

Correct option is

A

u

2πr

Let the velocity of the particle of mass m, after the collision is u

1

and the velocity of the particle of mass 2m is u

2

.

From conservation of momentum, it can be written as,

mu=mu

1

+2mu

2

u=u

1

+2u

2

Since, the collision is elastic, the kinetic energy is conserved in the collision and it can be written as,

2

1

mu

2

=

2

1

mu

1

2

+

2

1

2mu

2

2

u

2

=u

1

2

+2u

2

2

u

2

−u

1

2

=2u

2

2

(u−u

1

)(u+u

1

)=2u

2

2

(u+u

1

)=u

2

u=u

2

−u

1