In a system of particle 8 kg mas is subjected to a force of 16 N along +ve y-axis and another 8 kg mass is subjected to a force of 8 N along +ve x-axis. The magnitude of acceleration of the 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)//2 ms^(-2), theta=tan^(-1)(2)`
D. `1ms^(-2), theta=tan^(-1)sqrt(3)`

Answer

C

Explanation

`F_(ext)=sqrt(F_(x)^(2)+F_(y)^(2))=sqrt(16^(2)+8^(2)))=8sqrt(5)N`
`M=m_(1)+m_(2)=8+8=16 therefore vec(F)_(ext)=Mvec(a)_(CM)`
`abs(vec(a)_(CM))=abs(vec(F)_(ext))/M=(8sqrt(5))/16=sqrt(5)/2m//sec^(2)`
`vec(a)_(CM)` lies in the direction of `vec(F)_(ext)` Angle made by `vec(F)_(ext)` with x-axis.
`=tan^(-1)""F_(y)/F_(x)=tan^(-1)""16/8=tan^(-1)(2)`