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Two bodies of mass 1 kg and 3 kg have po...

Two bodies of mass `1 kg` and `3 kg` have position vectors `hat i+ 2 hat j + hat k` and `- 3 hat i- 2 hat j+ hat k`, respectively. The centre of mass of this system has a position vector.

A

`-2hati-hatj+hatk`

B

`2hati-hatj+hatk`

C

`-hati+hatj+hatk`

D

`-2hati+2hatk`

Text Solution

Verified by Experts

The correct Answer is:
A
Give : `m_(1)=1 kg, vec(r_(1))=hat(i)+2hat(j)+hat(k)`
`m_(2)=3 kg, vec(r_(2))=-3hat(i)-2hat(j)+hat(k)`
`r_(cm)=(m_(1)vec(r_(1))+m_(2)vec(r_(2)))/(m_(1)+m_(2))`
`=(1(hat(i)+2hat(j)+hat(k))+3(-3hat(i)-2hat(j)+hat(k)))/(1+3)`
`=(hat(i)+2hat(j)+hat(k)-9hat(i)-6hat(j)+3hat(k))/(4)`
`=(-8hat(i)-4hat(j)+4hat(k))/(4)`
`therefore r_(cm)=-2hat(i)-hat(j)+hat(k)`
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