Two bodies A and B of masses 5.00 kg and 10.0 kg respectively moving in opposite directions with velocities 4.00 m/s and 0.50 m/s respectively make head-on collision in free space. The force of their mutual interaction varies according to the given graph. Select incorrect statement.

Options

A. Period of deformation is 0.20 s.
B. Coefficient of restitution is 0.4.
C. Body A will move with velocity 0.5 m/s in the original direction.
D. Body B will move with velocity 1.75 m/s in the opposite direction.

Answer

C

Explanation

Common velocity at maximum deformation
`v_("common")=(5xx4+10xx(-0.2))/(5+10)=1m//s`
Change in momentum of 5 kg ball in deformation period `=5[4-1]=15 kgm//s`
In this period impulse
`=(1)/(2)(150)t=15rArrt=0.20s`
Therefore period of deformation `=0.20s` and period of recovery`=0.30-0.20=0.10s`
Coefficient of restitution
`=("Inpulse of recovery")/("Impulse of deformation")=(0.10)/(0.20)=(1)/(2)`
Final velocity of body A
`=(5xx1-(1)/(2)xx150xx0.1)/(5)=-0.5m//s`
Final velocity of body B `=(10xx1+(1)/(2)xx150xx0.1)/(10)=+1.75 m//s`