- #1

Satvik Pandey

- 591

- 12

## Homework Statement

A large sphere rests on a rough horizontal ground,

A ball of mass 'm' is thrown towards it along one of its radius at a speed 'u' , along an angle 'x' with the vertical

Find the angle with the vertical at which the ball should strike (find x) so that the large sphere pure rolls immediately after collision.

coefficient of friction=1

mass of large sphere = 1

radius of large sphere = sqroot(0.4)

## Homework Equations

## The Attempt at a Solution

During collision impulse will [/B]act in direction perpendicular to the contact surface. As the contact surface is the tangent of the sphere so the acting impulse will pass through the center of the sphere.

As the sphere do not jumps after the collision so ##J_{n}+mg=Jcos(x)##. Now mg is very small as compared to these impulses so I can assume

##J_{n}=Jcos(x)##...(1)

Let ##v## be the velocity of the com of the sphere after collision so

##Jsinx-Jcosx=mv## (value of ##\mu## is 1)...(3)

Angular impulse will only be provided by the friction force.

So ##Jcos(x)R=I_{CoM}\omega##...(4)

As the sphere rolls after collision so ##v=R\omega##

Solving these equations gives wrong answer.Are my equations correct?