Two particles whose masses are 10 kg and 30 kg and their position vectors are `hati+hatj+hatk and -hati-hatj-hatk` respectively would have the centre of mass at position :-

Options

A. `((hati+hatj+hatk))/(2)`
B. `((hati+hatj+hatk))/(2)`
C. `((hati+hatj+hatk))/(4)`
D. `((hati+hatj+hatk))/(4)`

Answer

A

Explanation

`because vecR_(cm)=(m_(1)vecr_(1)+m_(2)vecr_(2))/(m_(1)+m_(2))`
`=(10(hati+hatj+hatk)+30(-hati-hatj-hatk))/(10+30)`
`(10hati+10hatj+10hatk-30hati-3hatj-30hatk)/(40)`
`=(-20hati-20hatj-20hatk)/(40)`
`vecR_(cm)=(-(hati+hatj+hatk))/(2)`.