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Two identical spheres each of mass M and...

Two identical spheres each of mass M and Radius R are separated by a distance 10R. The gravitational force on mass m placed at the midpoint of the line joining the centres of the spheres is

A

zero

B

`(2GMm)/(25R^(2))`

C

`(GMm)/(25R^(2)`

D

`(GMm)/(100R^(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) The situation is as shown in the figure.

Let P is the midpoint of the line joining the centres of the spheres.
The gravitational force on mass m due to sphere A is
`F_(1)=(GMm)/((5R)^(2))` along `PO_(1)`
The gravitational force on mass m due to sphere B is
`F_(2)=(GMm)/((5R)^(2))` along `PO_(2)`
Net force on mass is
`F_R=F_(1)-F_(2) ( :. F_(1) " and " F_(2) " are opposite in direction ")`
`=(GMm)/((5R)^(2))-(GMm)/((5R)^(2))=0`
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