Question

Two masses of 10 kg and 20 kg are connected by a massless spring. A force of 200 N acts on the 20 kg mass away from the spring. At a certain instant, the acceleration of 10 kg mass is 12 m/s${}^2$. The acceleration of the 20 kg mass at that instant is

• A. $12m/s^2$
• B. $10m/s^2$
• C. $4m/s^2$
• D. $2m/s^2$

Answer 1

The correct option is C $4m/s^2$

Let, $a_1,a_2$ are the acceleration of masses $m_1,m_2$ at instant $t$ and let $F$ be the force acts on the mass $m_2$.

So the equation of motion of the system, $F=m_1{a}_1+m_2{a}_2$
Given, $m_1=10kg,m_2=20kg,a_1=12m/s^2,F=200N$
$\therefore$ $200=10\times 12+20a_2$
$20a_2=200-120=80$
$a_2=4m/s^2$