Gravitation Question 369
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}] $ as . The gravitational field due to the ring at a distance $ [\sqrt{3}r] $ is.
Options:
A) $ [\frac{Gm}{8r^{2}}] $
B) $ [\frac{Gm}{4r^{2}}] $
C) $ [\sqrt{3}\frac{Gm}{8r^{2}}] $
D) $ [\frac{Gm}{8r^{2}\sqrt{3}}] $
Show Answer
Answer:
Correct Answer: C
Solution:
-
The gravitational field due to the ring at a distance $ [\sqrt{3}r] $
is given by $ [E=\frac{Gm(\sqrt{3})}{{{\left[ r^{2}+{{(\sqrt{3}r)}^{2}} \right]}^{3/2}}}\Rightarrow E=\frac{\sqrt{3}Gm}{8r^{2}}] $
