In a system of particles 8 kg mass 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. `sqrt5//2ms^(-2), theta=45^@`
B. `3sqrt5ms^(-2), theta=tan^(-1)(2//3)`
C. `sqrt5//2ms^(-2),theta=tan^(-1)(2)`
D. `1ms^(-2),theta=tan^(-1)sqrt3`

Answer

C

Explanation

`F_(ext)=sqrt(F_x^2+F_y^2)=sqrt(16^2+8^2)=8sqrt5N`
`M=m_1+m_2=8+8=16:. vecF_(ext)=Mveca_(CM)`
`|veca_(CM)|=|(|vecF_(ext)|)/M=(8sqrt5)/16 = sqrt5 /2 m//sec^2`
`veca_(CM)` lies in the direction of `vecF_(ext)` Angle made by `vecF_(ext)` with x - axis.
`=tan^(-1)""(F_y)/(F_x)=tan^(-1)""(16)/8=tan^(-1)(2)`