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)(4hat(i)+6hat(j)-3hat(k))`
B. `(1)/(7)(18hat(i)+17hat(j)-3hat(k))`
C. `(1)/(7)(6hat(i)+4hat(j)-6hat(k))`
D. `(1)/(7)(9hat(i)+8hat(j)-6hat(k))`

Answer

B

Explanation

`m_1=3 kg, m_2=4kg`
`v_1 =(2 hat(i)+3hat(j)+3hat(k))`
`v_2 =(3hat(i)+2hat(j)-3hat(k)) m//s`
`m_1v_1+m_2v_2=(m_1+m_2)`
`v=(m_1 v_1+m_2v_2)/(m_1+m_2)`
`=(3[2hat(i)+3hat(j)+3hat(k)]+4[3hat(i)+2hat(j)-3hat(k)])/(3+4)`
`=(6hat(i)+9hat(j)+9hat(k)+12hat(i)+8hat(j)-12hat(k))/(7)`
`=(18hat(i)+17hat(j)-3hat(k))/(7)`.