Question

A body of mass m makes an elastic collision with another identical body at rest. Show that if the collisionis not head on the bodiese to at right to each other after the collision.

Answer 1

Correct Answer - A
Sicne it is not a head on collision the two bodies move in different dimensions.
Let `v_1,v_2rarr `velocities of the bodies vector collision.
Sicne the collision is elastic applyig law of conservation of momentum on X
=direction
`mu_1+mxx0=mv_1cosalpha+mv_2cosbeta`
`rarr v_1cosalpha+v_2cosbeta=u_1`......i
Putting law of conservation of momentum in y direction
`O=mv_1siN/Alphav_2sinbeta`....ii
` Again (1/2)mu_1^2+0=-(1/2)mv_2^2+(1/2)mxxv_2^2`
`rarr u_1^2=v_1^2+v_2^2`........iii
`squaring eqution i
`v_1^2+v_2^2`...........iii ltbr.gt square equation i
`v_1^2+v_2^2=`
`v_1^2cos^2alpha+v_2^2cos^2beta+2v_1v_2cosalphacosbeta`
`rarr v_1^2sin^2alpha+v_2^2sin^2beta+2v_1v_2cosalphacosbeta`
`rarr 2v_1^2sin^2alpha=2xxv_1xx(v_1siN/Alpha)/(sinbeta)cosalpha cosbeta`
`rarr siN/Alpha sinbeta=cosalphacosbeta`
`rarr cosalpha.cosbeta-siN/Alphacosbeta=0`
`cos(alpha+beta)=0=cos90^0`
`rarr alpha+beta=90^0`