A body of mass 3kg moving with a velocity `(2 hat(i) + 2 hat(j) + 3 hat(k))` m/s collides with another body of mass 4kg moving with a velocity `(3 hat(i) + 2 hat(j) - 3 hat(k))` m/s. The two bodies stick together after collision. The velocity of the composite body is

Options

A. `(1)/(7) (4 hat(j) + 6 hat(j) - 3 hat(k))`
B. `(1)/(7) (18 hat(i) + 14 hat(j) - 3 hat(k))`
C. `(1)/(7) (6 hat(i) + 4 hat(j) - 6 hat(k))`
D. `(1)/(7) (9 hat(i) + 8 hat(j) - 6 hat(k))`

Answer

b

Explanation

Given, mass of first body `(m_(1)) = 3kg`
velocity of first body `(v_(1)) = (2 hat(i) + 3 hat(j) + 3 hat(k))` m/s
mass of second body `(m_(2)) = 4kg`
velocity of second body `(v_(2)) = (3 hat(i) + 2 hat(j) - 3 hat(k))` m/s
According to law of conversion of linear momentum,
`m_(1)v_(1) + m_(2)v_(2) = (m_(1) + m_(2)) V`
`implies (2 hat(i) + 2 hat(j) + 3 hat(k)) 3 + (3 hat(i) + 2 hat(j) - 3 hat(k)) 4 = ( 4 + 3) V`
`implies 6 hat(i) + 9 hat(j) + 9 hat(k) + 12 hat(j) + 8 hat(j) - 12 hat(k) = 7V`
`implies 18 hat(i) + 17 hat(j) - 3 hat(k) = 7V`
`implies v = (1)/(7) (18 hat(i) +17 hat(j) - 3 hat(k))`