Question

A spring is compressed between two toy carts of mass $m_1$ and $m_2$. When the toy carts are released, the springs exert equal and opposite average forces for the same time on each toy cart. If $V_1$ and $V_2$ are the velocities of the toy carts and there is no friction between the toy carts and the ground, then :

• A. $V_2 / V_2 = m_1 / m_2$
• B. $V_1 / V_1 = m_2 / m_1$
• C. $V_1 / V_2 = - m_2 / m_1$
• D. $V_1 / V_2 = m_1 / m_2$

Answer 1

The Correct Option is C

Here, $m_{1} \frac{d V_{1}}{d t}=-m_{2} \frac{d V_{2}}{d t}$ or $m_{1} a_{1}=m_{2} a_{2} \ldots$ (1) now, $V_{1}=a_{1} t$ and $V_{2}=a_{2} t$ (by using $v=u+$ at) from (1), $m _{1} \frac{ V _{1}}{ t }=- m _{2} \frac{ V _{2}}{ t }$ $\therefore \frac{ V _{1}}{ V _{2}}=-\frac{ m _{2}}{ m _{1}}$