A) \[mgR\]
B) \[\frac{mgR}{2}\]
C) \[\frac{mgR}{4}\]
D) \[\frac{3mgR}{4}\]
Correct Answer: C
Solution :
[c] Conserving momentum during the explosion \[mv=\frac{m}{2}\times 0+\frac{m}{2}v'\] or \[v'=2v\] Increase in the mechanical energy \[=\Delta K+\Delta U=\Delta K+0=\frac{1}{2}\frac{m}{2}{{\left( 2v \right)}^{2}}-\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m{{v}^{2}}\]\[=\frac{GMm}{4R}=\frac{mgR}{4}\left[ v=\sqrt{\frac{GM}{2R}} \right]\]
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