wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A uniform sphere of mass M and radius R is surrounded by a concentric spherical shell of same mass but radius 2R. A point mass m is kept at a distance x(>R) in the region bounded by spheres as shown in the figure. The net gravitational force on the particle is


A

GMmx2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

GMmxR3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

G(M+m)x2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
zero
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A
GMmx2
The gravitational force on the point mass m due to uniform sphere is F=GMmx2 Where,
x is the distance between centre of sphere and mass m.

M is the mass of sphere.

The net gravitational force on the point mass due to the outer spherical shell will be zero because the gravitational force of attraction on a point mass due to various points of the spherical shell cancel each other completely as their vector sum is zero.

Thus, the net gravitational force on the particle will be F=GMmx2.

Key Concept:
Field due to uniform solid sphere of mass M and radius R at distance r outside of sphere is GM/r2 and inside of the sphere is GMr/R3.

Field due to uniform hollow sphere of mass M and radius R at r outside the sphere is GM/r2 and inside is=0.
Why this question : It is absolutely important to be well versed with the field due to a solid sphere and a hollow sphere on both sides inside and outside. This concept is extremely important from a JEE standpoint.

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon