SATHEE: Gravitation Question 224

Gravitation Question 224

Question: A uniform ring of mass $[m]$ and radius r is placed directly above a uniform sphere of mass $[M]$ and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance $[r \sqrt{3}]$ $[r]$ as . The gravitational force exerted by the sphere on the ring will be

Options:

A) $[\frac{G M m}{8 r^{2}}]$

B) $[\frac{G M m}{4 r^{2}}]$

C) $[\sqrt{3} \frac{G M m}{8 r^{2}}]$

D) $[\frac{G M m}{8 r^{2} \sqrt{3}}]$

Show Answer

Answer:

Correct Answer: C

Solution:

$[d F = G \frac{M d m}{4 r^{2}}]$ $[F = Σ d F \cos θ]$

$[= Σ \frac{G M d m}{4 r^{2}} \cos θ]$

$[= \frac{G M}{4 r^{2}} \times \frac{\sqrt{3 r}}{2 r} Σ d m]$

$[= \frac{\sqrt{3} G M m}{8 r^{2}}]$

Alternative solution:

The gravitational field due to the ring at a distance $[E = \frac{G m (\sqrt{3 r})}{{[r^{2} + {(\sqrt{3} r)}^{2}]}^{3 / 2}}]$

or E= $[\frac{\sqrt{3} G m}{8 r^{2}}]$ The required force is EM, i.e., $[(\sqrt{3} G m) M / 8 r^{2}]$ .

Play Store

App Store

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Gravitation Question 224

Question: A uniform ring of mass [m] and radius r is placed directly above a uniform sphere of mass [M] and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance [r3] [r] as . The gravitational force exerted by the sphere on the ring will be

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu