Gravitation Question 325
Question: Consider two solid uniform spherical objects of the same density p. One has radius R and the other has radius 2R. They are in outer space where the gravitational field from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction?
Options:
A) $ [G{{\pi }^{2}}R^{2}] $
B) $ [\frac{128}{81}G{{\pi }^{2}}R^{4}{{\rho }^{2}}] $
C) $ [\frac{128}{81}G{{\pi }^{2}}] $
D) $ [\frac{128}{81}{{\pi }^{2}}R^{4}G] $
Show Answer
Answer:
Correct Answer: B
Solution:
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$ [{m_{1}} =\frac{4}{3}\pi R^{3}\rho , m_{2} =\frac{4}{3}\pi {{\left( 2R \right)}^{3}}\rho ] $ , distance between the centres of the two spherical objects, $ [r=3R.] $
$ [F=\frac{GM_{1}m_{2}}{r^{2}}] $
$ [=G\left( \frac{4}{3}\pi R^{3}\rho\right)\left( 8\times \frac{4}{3}\pi R^{3}\rho\right)\times \frac{1}{{{\left( 3R \right)}^{2}}}] $ $ [=\frac{128}{81}G{{\pi }^{2}}R^{4}{{\rho }^{2}}] $
