1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# A uniform sphere of mass M and radius R exerts a force F on a small mass m situated at a distance of 2R from the centre O of the sphere. A spherical portion of diameter R is cut from the sphere as shown in the figure. The force of attraction between the remaining part of the sphere and the mass m will be

A

7F9

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

2F3

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C

4F9

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D

F3

No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is A 7F9 The force of attraction between the complete sphere and mass m is F=GmM(2R)2=GmM4R2 Mass of complete sphere is M=4π3R3ρ, where ρ is the density of the sphere. Mass of the cut-out portion is m0=4π3(R2)2ρ=M8. Now, the distance between the centre of the cut out portion and mass m =2R−R2=3R2 Hence, the force of attraction between the cut out portion and mass m is f=Gm0m(3R2)2=G(M8)m9R24=GmM4R2×29=2F9 Therefore, the force of attraction between the remaining part of the sphere and mass m =F−f=F−2F9=7F9 which is choice (a).

Suggest Corrections
1
Join BYJU'S Learning Program
Related Videos
Gravitation Field
PHYSICS
Watch in App
Explore more
Join BYJU'S Learning Program