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JIPMER 2015
Exam
JIPMER
Year
2015
Subject
Physics
Chapter
Gravitation

JIPMER 2015 · Physics · Gravitation

A uniform ring of mass m and radius a is placed directly above a...

A uniform ring of mass mm and radius aa is placed directly above a uniform sphere of mass MM and of equal to radius. The centre of the ring is at a distance 3a\sqrt{3} a from the centre of the sphere. The gravitational force (F)(F) exerted by the sphere on the ring isA uniform ring of mass m and radius a is placed directly above a uniform sphere of mass M and of equal to radius. The

Options

  1. A3GMm8a2\frac{\sqrt{3} G M m}{8 a^2}
  2. B2GMm3a2\frac{2 G M m}{3 a^2}
  3. C7GMm2a2\frac{7 \mathrm{GMm}}{\sqrt{2} a^2}
  4. D3GMma2\frac{3 G M m}{a^2}

Correct answer

A. 3GMm8a2\frac{\sqrt{3} G M m}{8 a^2}

Step-by-step solution

Now, the gravitational field due to the ring at a distance d=3ad=\sqrt{3} a on its axis is E=Gmd(a2+d2)3/2=3Gm8a2E=\frac{G m d}{\left(a^2+d^2\right)^{3 / 2}}=\frac{\sqrt{3} G m}{8 a^2} A uniform ring of mass m and radius a is placed directly above a uniform sphere of mass M and of equal to radius. The The force in a particle of mass MM placed here is F=ME=3GMm8a2F=M E=\frac{\sqrt{3} G M m}{8 a^2} This is also the force due to the sphere in the ring.
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