Find the yelocity of centre of mass of the system shown the figure:

Options

A. `((2+2sqrt3)/3)hati-2/3hatj`
B. `(2hati+2sqrt3hatj)/3`
C. `((2-2sqrt3)/3)hati-2/3hatj`
D. None of these

Answer

A

Explanation

Here , `m_i =1 kg ,v_1 =2hati`
`m_2=2kg, v_2 = 2cos 30hati -2 sin 30hatj`
`v_(CM)=(m_1v_1+m_2v_2)/(m+m_2)=(1xx2hati+2(2cos30hati-2sin30hatj))/(1+2)=(2hati+2sqrt3hati-2hatj)/3=((2+2sqrt3)/3)hati-2/3hatj`