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Tension in a String

If a force ...

Question

If a force $F_{1}$ is applied on $m_{1}$ towards east and $F_{2}$ on $m_{2}$ towards west, then the contact force between $m_{1}$ and $m_{2}$ is $(F_{1} > F_{2})$

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

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

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

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

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Solution

The correct option is B $\frac{m_{1} F_{2} + m_{2} F_{1}}{m_{1} + m_{2}}$
$a c c = \frac{F_{1} - F_{2}}{m_{1} + m_{2}}$
$F_{1} - N = m_{1} (\frac{F_{1} - F_{2}}{m_{1} + m_{2}})$
$\Rightarrow N = \frac{m_{2} k_{1} + m_{1} k_{2}}{m_{1} + m_{2}}$
Hence,
option $(B)$ is correct answer.

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If a force F1 is applied on m1 towards east and F2 on m2 towards west, then the contact force between m1 and m2 is (F1>F2)

The correct option is B m1F2+m2F1m1+m2acc=F1−F2m1+m2F1−N=m1(F1−F2m1+m2)⇒N=m2k1+m1k2m1+m2Hence,option (B) is correct answer.

If a force $F_{1}$ is applied on $m_{1}$ towards east and $F_{2}$ on $m_{2}$ towards west, then the contact force between $m_{1}$ and $m_{2}$ is $(F_{1} > F_{2})$

The correct option is B $\frac{m_{1} F_{2} + m_{2} F_{1}}{m_{1} + m_{2}}$
$a c c = \frac{F_{1} - F_{2}}{m_{1} + m_{2}}$
$F_{1} - N = m_{1} (\frac{F_{1} - F_{2}}{m_{1} + m_{2}})$
$\Rightarrow N = \frac{m_{2} k_{1} + m_{1} k_{2}}{m_{1} + m_{2}}$
Hence,
option $(B)$ is correct answer.