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

Options

A. (a) `(1.5,-1,-2)`
B. (b) `(1.5,-2,-2)`
C. (c) `(1.5,-1,-1)`
D. (d) None of these

Answer

D

Explanation

At `5s`
`r_(COM)=r_i+v_(CM)t`
`=(hati)+(0.2xx5)hati`
`=2hati=(m_1r_i+m_2r_2)/(m_1+m_2)`
`:. 2hati=((2//3)(3hati+2hatj--4hatk)+(4//3)r_2)/(2)`
`:. r_2=(4.5hati-hatj-2hatk)`
So, the co-ordinates are `(4.5m, -1m, -2m)`