A) g
B) \[\frac{g}{2}\]
C) \[\frac{3g}{4}\]
D) \[\frac{g}{\sqrt{2}}\]
Correct Answer: B
Solution :
The acceleration of the centre of mass of the block \[=\left| \frac{m{{{\vec{a}}}_{1}}+m{{{\vec{a}}}_{2}}}{m+m} \right|\,=\frac{1}{2}\,\sqrt{a_{1}^{2}\,+a_{2}^{2}}\] \[=\frac{g}{2}\,\sqrt{{{(\sin \,\angle \,ABC)}^{2}}\,+{{(\sin \,\angle ACB)}^{2}}}\] \[=\frac{g}{2}\,\sqrt{{{\sin }^{2}}\,{{30}^{0}}\,+{{\sin }^{2}}\,{{60}^{0}}}\] \[=\frac{g}{2}\,\sqrt{{{(0.5)}^{2}}\,+{{(0.866)}^{2}}}=\frac{g}{2}\]
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