A body of mass 2 g, moving along the positive x-axis in gravity free space with velocity `20 cms^(-1)` explodes at x=1m,t=0 into two pieces of masses `2/3` and `4/3` After 5 s, the lighter piece is at the point (3m, 2m, -4m). Then the position of the heavier piece at this moment, in metrės 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
`vecr_(COM)=vec(r_i)+vecv_(CM)t=(hati)+(0.2xx5)hati=2hati=(m_1vecr_1+m_2vecr_2)/(m_1+m_2)`
`:.2hati=((2/3xx3hati+2/3xx2hatj-2/3xx4hatk)+4/3r)/2`
`4hati=2hati+4/3hatj-8/3hatk+4/3vecr`
`4/3 vecr=2hati-4/3hatj+8/3hatk`
`vecr=1.5 hati-hatj+2hatk`
`vecr=1.5hati-hatj+2hatk `
So , the co-ordinates are (1.5,-1.2) .