Question

If Gravitational field due to uniform thin hemispherical shell at point $P$ is $I$, then the magnitude of gravitational field at $Q$ is (Mass of hemisphere is $M$, radius $R$) -

• A. $\frac{GM}{4R^2}-I$
• B. $\frac{GM}{4R^2}+I$
• C. $\frac{GM}{4R}-I$
• D. $2I-\frac{GM}{2R^2}$

Answer 1

Answer: (A)

$\frac{GM}{4R^2}-I$

The gravitational field at P and Q due to the whole sphere is given as $\frac{GM}{4R^2}$.
As the gravitational field due to the hemispherical shell at point P is I, using symmetry the gravitational field due to the imaginary hemispherical shell at point Q would also be I.
Thus the gravitational field due to the given hemisphere at point Q will be
(Gravitational field due to whole sphere at Q)-(Gravitational field due to imaginary hemisphere at Q)
$=\frac{GM}{4R^2}-I$