JEE Main & Advanced
Physics
Gravitation / गुरुत्वाकर्षण
Question Bank
Self Evaluation Test - Gravitation
question_answer
In older times, people used to think that the earth was flat. Imagine that the earth is indeed not a sphere of radius R, but an infinite plate of thickness H. What value of is needed to allow the same gravitational acceleration to be experienced as on the surface of the actual earth? (Assume that the earth's density is uniform and equal in the two models
A)2R/3
B)4R/3
C)8R/3
D)R/3
Correct Answer:
A
Solution :
[a] Gauss law for gravitation \[\int{\vec{g}.d\vec{s}=-{{\operatorname{m}}_{in}}.4\pi G;g=\frac{GM}{{{R}^{2}}}}\] \[2\times \frac{GM}{{{R}^{2}}}\times A=\frac{M}{\frac{4}{3}\pi {{R}^{3}}}\left( h\times A \right)\times 4\pi G\] \[\Rightarrow h=\frac{2R}{3}\]