In a system of particles `8 kg` mass is subjected to a force of `16 N` along + ve `x`-axis and another `8 kg` mass is subjected to a force of `8 N` along + ve ` y`-axis. The magnitude of acceleration of centre of mass and the angle made by it with `x`-axis are given, respectively, by

Options

A. `(sqrt(5))/2ms^(2),theta=45^(@)`
B. `3sqrt(5)ms^(2),theta=tan^(-1)(2/3)`
C. `(sqrt(5))/2ms^(2),theta=tan^(-1)(1/2)`
D. `1ms^(2),theta=tan^(-1)sqrt(3)`

Answer

C

Explanation

`veca_(CM)=vecF/(m_(1)+m_(2))=(16hati+8hatj)/(8+8)=hati+1/2hatj`
`|veca(CM)|=sqrt(1^(2)(1/2)^(2))=sqrt5/2m//s^(2)`
`tantheta=(a_(y))/(a_(x))=(1/2)/1=1/2impliestheta=tan^-(1)(1/2)`