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 hemispherical shell is M, radius is R )

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 hemispherical shell is M, radius is R ) <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-qkciadndccie.png" /> (A) (G M/2 R2)-I (B) (G M/2 R2)+I (C) (G M/4 R)-I (D) 2I -(G M/2 R2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-qkciadndafoe.png" /> gravitational field due to II at P = gravitational field at I at Q At P , EI+EII=(G (2 m)/(2 R)2)=(G M/2 R2) EI=(G M/2 R2)-EII=(G M/2 R2)-I

Q. 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 hemispherical shell is $M,$ radius is $R$ )

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

$\frac{GM}{2 R ^{2}} + I$

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

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

gravitational field due to $II$ at $P$ = gravitational field at $I$ at $Q$
At $P$ ,
$E_{I} + E_{II} = \frac{G ( 2 m )}{( 2 R ) ^{2}} = \frac{GM}{2 R ^{2}}$
$E_{I} = \frac{GM}{2 R ^{2}} - E_{II} = \frac{GM}{2 R ^{2}} - I$

Q. 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 hemispherical shell is M, radius is R )

2R2GM​−I

2R2GM​+I

4RGM​−I

2I −2R2GM​