A 2 kg ball moving at 24 m s -1 undergoes head on collision with a 4 kg ball moving in the opposite direction at 48 m s -1 . If the coefficient of restitution is (2/3), their velocities in m s -1 after collision are

Question

A 2 kg ball moving at 24 m s -1 undergoes head on collision with a 4 kg ball moving in the opposite direction at 48 m s -1 . If the coefficient of restitution is (2/3), their velocities in m s -1 after collision are (A) -56, -8 (B) -28, -4 (C) -14, -2 (D) -7, -1

Tardigrade Admin · Accepted Answer

Here, m1=2 kg , m2=4 kg =2 m 1 u1=24 m s -1, u2=-48 m s -1=-2 u1 where u1 and u2 be the velocities of masses m1 and m2 before collision. Let v1 and v2 be the velocities of masses m1 and m2 after collision. According to the law of conservation of linear momentum, we get m1 u1+m2 u2=m1 v1+m2 v2 ; m1 u1+2 m1(-2 u1) =m1 v1+2 m1 v2 -3 u1=v1+2 v2 dots(i) Coefficient of restitution, e=(v2-v1/u1-u2) v2-v1=e(u1-u2)=e(u1-(-2 u1)) v2-v1=3 u1 e dots(ii) Adding (i) and (ii), we get 3 v2=3 u1 e-3 u1 or v2=u1(e-1) dots(iiI) Substituting this value of v2 in (i), we get v1=-u1(1+2 e) dots(iv) Substituting the given values in (iii) and (iv), we get v2=24((2/3)-1)=-8 m s -1 and v1=-24(1+2 × (2/3))=-56 m s -1

Q. A 2kg ball moving at 24ms−1 undergoes head on collision with a 4kg ball moving in the opposite direction at 48ms−1. If the coefficient of restitution is 32​, their velocities in ms−1 after collision are

-56, -8

-28, -4

-14, -2

-7, -1

Q. A $2 k g$ ball moving at $24 m s^{- 1}$ undergoes head on collision with a $4 k g$ ball moving in the opposite direction at $48 m s^{- 1} .$ If the coefficient of restitution is $\frac{2}{3},$ their velocities in $m s^{- 1}$ after collision are