Question

Two masses $m_{1}=1 \, kg$ and $m_{2}=2kg$ are connected by means of a light inextensible string which passes over a weightless pulley as depicted in the figure. If both the masses start from rest, the distance travelled by the center of mass in two seconds will be(Take $g=10 \, m \, s^{- 2}$ )

• A. $\frac{20}{9}m$
• B. $\frac{40}{9}m$
• C. $\frac{2}{3}m$
• D. $\frac{1}{3}m$

Answer 1

Answer: (A)

Here, $m_{1}=1kg, \, m_{2}=2 \, kg$
The acceleration of the system
$a=\frac{\left(\right. m_{2} - m_{1} \left.\right) g}{m_{1} + m_{2}}=\frac{\left(\right. 2 - 1 \left.\right) g}{\left(\right. 1 + 2 \left.\right)}=\frac{g}{3}=\frac{10}{3}$
Acceleration of the centre of mass is
$a_{C M}=\frac{1 \left(\frac{- g}{3}\right) + 2 \left(\frac{g}{3}\right)}{3}=\frac{g}{9}=\frac{10}{9}$
The distance travelled by the centre of mass in two seconds is
$s=\frac{1}{2}a_{C m}t^{2}=\frac{1}{2}\times \frac{10}{9}\times \left(2\right)^{2}=\frac{20}{9}m$