Question

Two blocks of masses $m_{1}$ and $m_{2}$ being connected with a light spring of stiffness $k$ are driven with forces $F_{1}$ and $F_{2}$ on a smooth horizontal plane. If the blocks move with same acceleration $a_{0},$ the value of $a_{0}$ is:-

• A. $\frac{F_{1} - F_{2}}{ m_{1} + m_{2}}$
• B. $\frac{F_{1} m_{2} - m_{1} F_{2}}{\left( m_{1} + m_{2}\right)^{2}}$
• C. $\frac{1}{2}\left(\frac{F_{1}}{ m_{1}} + \frac{F_{2}}{ m_{2}}\right)$
• D. decided by the stiffness of the spring

Answer 1

Answer: (A)

In the given system, the spring force due to spring on the masses is internal force. The acceleration of system is due to external forces only. Here we can assume the two blocks as one system and their acceleration is given as
$a_{0}=\frac{\text{Net force towards motion of masses}}{\text{Total mass}}$
$a_{0}=\frac{F_{1} - F_{2}}{m_{1} + m_{2}}$ .