A) \[{{\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)}^{2}}g\]
B) \[\frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}g\]
C) \[\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}-{{m}_{2}}}g\]
D) Zero
Correct Answer: A
Solution :
Acceleration of each mass \[=a=\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)\ g\] Now acceleration of centre of mass of the system \[{{A}_{cm}}=\frac{{{m}_{1}}\overrightarrow{{{a}_{1}}}+{{m}_{1}}\overrightarrow{{{a}_{2}}}}{{{m}_{1}}+{{m}_{2}}}\] As both masses move with same acceleration but in opposite direction so \[\overrightarrow{{{a}_{1}}}=-\overrightarrow{{{a}_{2}}}\] = a (let) \[\therefore \ \ {{A}_{cm}}=\frac{{{m}_{1}}a-{{m}_{2}}a}{{{m}_{1}}+{{m}_{2}}}\] \[=\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)\times \left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)\times g\] \[={{\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)}^{2}}\times g\]You need to login to perform this action.
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