A) \[{{F}_{3}}={{F}_{1}}+F{{ }_{2}}\]
B) \[{{F}_{3}}=\frac{{{m}_{3}}F}{{{F}_{1}}+F{{ }_{2}}+{{F}_{3}}}\]
C) \[{{F}_{3}}=\frac{{{m}_{3}}F}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}}\]
D) \[\,{{F}_{3}}=\frac{{{m}_{3}}F}{{{m}_{1}}+{{m}_{2}}}\]
Correct Answer: C
Solution :
[c] Common acceleration of system is \[a=\frac{F}{{{m}_{1}}+{{m}_{2}}+{{m}_{3}}}\] \[\therefore \text{ Force on }{{m}_{3}}\text{ is }{{F}_{3}}={{m}_{3}}\times a\] \[=\frac{{{m}_{3}}F}{{{m}_{1}}+{{m}_{2}}+m}\]
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