Two objects of masses 200 g and 500 g possess velocities `10hati ms^(-1)` and `3hati+5hatj ms^(-1)` respectively. The velocity of their centre of mass in `ms^(-1)` is

Options

A. `5hati-25hatj`
B. `(5)/(7)hati-25hatj`
C. `5hati+(25)/(7)hatj`
D. `25hati-(5)/(7)hatj`

Answer

(c)

Explanation

`m_(1)=200g,m`,`m_(2)=500g`,
`v_(1)=10hati m//s`,`v_(2)=3hati+5hatj` (Given)
velocity of their centre of mass,
`v_(cm)=(m_(1)v_(1)+m_(2)v_(2))/(m_(1)+m_(2))=(200xx10hati+500(3hati+5hatj))/(200+500)`
`(2000hati+1500hati+2500hatj)/(700)`
`5hati+(25)/(7)hatj`