In a system of particles `8 kg` mass is subjected to a force of `16 N` along `+ve` x-axis and another `8 kg` 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))/(2) ms^-2, theta = 45^@`
B. `3sqrt(5) ms^-2, theta = tan^-1(2//3)`
C. `(sqrt(5))/(2) ms^-2, theta = tan^-1(1//2)`
D. `1 ms^-2, theta = tan^-1 sqrt(3)`

Answer

C

Explanation

( c) `m_1 x_1 = m_2 x_2`
`vec a_(cm) = (vec F)/(m) =(16 hat i + 8 hatj)/(16) = hat i + (1)/(2) hat j`
`|vec a_(cm)| = sqrt(1^2 + ((1)/(2))^2) = (sqrt(5))/(2) m//s^2`
`tan theta = (1//2)/(1) rArr theta = tan^-1 ((1)/(2))`.
.