A body of mass 2 g, moving along the positive x-axis in gravity free space with velocity 20 `cms^(-1)` explodes at x = 1 m, t = 0 into two pieces of masses `2/3g and 4/3g`. After 5 s, the lighter piece is at the point (3m, 2m, -4m). Then the position of the position of the heavier piece at this moment, in metres is

Options

A. (1.5, -1, -2)
B. (1.5, -2, -2)
C. (1.5, -1, -1)
D. (1.5, -1, +2)

Answer

D

Explanation

At 5 s
`vec_(r)_(COM)=vec(r)_(i)+vec(v)_(CM)=(hat(i))+(0.2 times 5)hat(i)=2hat(i)=(m_(1)vec(r)_(1)+m_(2)vec(r)_(2))/(m_(1)+m_(2))`
`therefore 2hat(i)=((2/3 times 3hat(i)+2/3 times 2hat(j)-2/3 times 4hat(k))+4/3r)/2`
`4hat(i)=2hat(i)+4/3hat(j)-8/3hat(k)+4/3hat(r)`
`4/3vec(r)=2hat(i)-4/3hat(j)+8/3hat(k)`
`vec(r)=1.5hat(i)-hat(j)+2hat(k)`
So, the co-ordinates are (1.5, -1, 2).