Two masses `m_1 = 1 kg and m_2 = 2 kg` are connected by a light inextensible string and suspended by means of a weightness pulley as shown in the figure. Assuming that both the masses start from rest, the distance travelled by the centre of mass in two seconds is `(Take g = 10 ms^-2`.
.

Options

A. `(20)/(9) m`
B. `(40)/(9) m`
C. `(2)/(3) m`
D. `(1)/(3)m`

Answer

A

Explanation

(a) Here, `m_1 = 1kg, m_2 = 2 kg`
The acceleration of the system is
`a = ((m_2 - m_1)g)/(m_1 + m_2) =((2 - 1)g)/((1 + 2))=(g)/(3) =(10)/(3)`
Acceleration of the centre of mass is
`a_(cm) =(m_1+ a_1 a_2)/(m_1 + m_2) = (1(-a) +2(a))/(1 + 2)`
=`(((-g)/(3)) + 2 ((g)/(3)))/(3) =(g)/(9) =(10)/(9)`
The distance travelled by the centre of mass in two seconds is
`S =(1)/(2) a_(cm) t^2 =(1)/(2) xx (10)/(9) xx (2)^2 = (20)/(9) m`.