question_answer

A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance '3a' from the centre will be: [JEE Main 9-4-2019 Morning]

A) \[\frac{2GM}{9{{a}^{2}}}\]                      

B) \[\frac{GM}{3{{a}^{2}}}\]

C) \[\frac{GM}{9{{a}^{2}}}\]                        

D) \[\frac{2GM}{3{{a}^{2}}}\]

Correct Answer: B

Solution :

We use gauss's Law for gravitation \[g.4\pi {{r}^{2}}=\](Mass enclosed)\[4\pi G\] \[g=\frac{3M4\pi G}{4\pi {{(3a)}^{2}}}\]\[=\frac{MG}{3{{a}^{2}}}\] Option [b]