Question

Two masses $m_1=4kg$ and $m_2=2kg$ are released from as shown in figure. Find
(i) The distance travelled by centre of mass in $9s$.
(ii) The speed of centre of mass after $9s$

Answer 1

Given that,

Mass $m_1=4kg$

Mass $m_2=2kg$

Now, the net force is

$F=m_{1}g-m_{2}g$

$F=4g-2g$

$F=2g$

$F=2\times 10$

$F=20N$

Now, the acceleration is

$F=ma$

$a=\frac{F}{m_1+m_2}$

$a=\frac{20}{6}$

$a=\frac{10}{3}m/s^2$

Now, the distance travelled in 9 sec

$s=ut+\frac{1}{2}a{t}^2$

$s=\frac{1}{2}\times \frac{10}{3}\times 81$

$s=135m$

Now, speed of center of mass after 9 s

$v=u+at$

$v=\frac{10}{3}\times 9$

$v=30m/s$

Hence, the distance is $135m$ and speed is $30m/s$