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Spring Force

Two blocks of...

Question

Two blocks of masses $m_{1}$ and $m_{2}$ are connected with a light spring of force constant $k$ and the whole system is kept on a frictionless horizontal surface. The masses are applied forces $F_{1}$ and $F_{2}$ as shown in figure. At any time, the blocks have same acceleration $a_{0}$ but in opposite directions.
Then acceleration $a_{0}$ is

A

\frac{F_{1} - F_{2}}{m_{1} + m_{2}}

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B

\frac{F_{1} - F_{2}}{m_{1} - m_{2}}

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C

\frac{F_{1} + F_{2}}{m_{1} - m_{2}}

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D

\frac{F_{1} + F_{2}}{m_{1} + m_{2}}

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Solution

The correct option is B $\frac{F_{1} - F_{2}}{m_{1} - m_{2}}$
FBD

Using Newtons second law $F_{n e t} = m_{1} a_{0} = F_{1} - k x$

Using Newtons second law $F_{n e t} = F_{2} - k x = m_{2} a_{0}$ (as per the question $a_{2} = a_{0}$ )

Subtracting the equations: $m_{1} a_{0} - m_{2} a_{0} = F_{1} - F_{2}$
$\Rightarrow a_{0} = \frac{F_{1} - F_{2}}{m_{1} - m_{2}}$

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