Two masses M and 3M collide on a horizontal frictionless surface as shown. Before the collision the mass M has a velocity `V_(1)` in the y-direction. The mass 3M has a velocity `(5//12)V_(0)` making an angle `thetha` to the x-axis as shown. After the collision the mass 3M comes to rest and the mass M moves along the x-axis with the velocity `V_(1)` (Given `sinthetha = 3//5`) Neglect gravity.

Options

A. The speed `V_(1)` of mass M before collision is `3/4 V_(0)`
B. The speed `V_(1)` of mass M before collision is `V_(0)/4`
C. The speed `V_(1)` of mass M after collision is `V_(0)/2`
D. The speed `V_(1)` of mass M after collision is `V_(0)`

Answer

A, D

Explanation

final momentum in y-axis is zero So `MV_(1)=(5/12V_(0)sintheta)3M`
`V_(1)=3/4V_(0)` Along x-axis initial momentum = final momentum `(5/12V_(0)costheta)3M=MV_(1)`
`V_(1)=V_(0)`