A) \[\left( \frac{n}{n+1} \right)mgR\]
B) \[\left( \frac{n}{n-1} \right)mgR\]
C) \[nmgR\]
D) \[\frac{mgR}{n}\]
Correct Answer: A
Solution :
Gravitational potential energy \[{{U}_{e}}=-\frac{GMm}{R}\] \[{{U}_{h}}=\frac{GMm}{(R+nR)}=-\frac{GMm}{R(n+1)}\] \[\Delta U={{U}_{h}}-{{U}_{e}}\] \[=\frac{GMm}{R}\left[ 1-\frac{1}{(n+1)} \right]\] \[=\frac{n}{(n+1)}\left[ \frac{GMm}{R} \right]\] \[=\frac{n}{(n+1)}mgR\]
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