Home
Class 11
PHYSICS
From a solid sphere of mass M and radius...

From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure Taking gravitational potential `V =0at r = oo,` the potential at (G = gravitational constatn)

A

`(-GM)/(2R)`

B

`(-GM)/(R)`

C

`(-2GM)/(3R)`

D

`(-2GM)/(R)`

Text Solution

Verified by Experts

The correct Answer is:
B
Potential at point P,
Due to complete solid sphere-
`V_("sphere")=(-GM)/(R^(3))[3R^(2)-(R/(2))^(2)]`
`=(-GM)/(R^(3))[(11R^(2))/(4)]=(-GMxx11)/(8R)`
Potential due to cavity-
`V_("cavity")=-(3)/(2)((GM)/(8))/(R//2)=(-3GM)/(8R)`
So, potential at centre of cavity
`V_("sphere")-V_("cavity")=(-11GM)/(8R)-((-3)/(8)(GM)/(R))=(-GM)/(R)`
Promotional Banner

Similar Questions

Explore conceptually related problems

From a solid sphere of mass M and radius R, a spherical portion of radiu (R )/(2) is removed as shown in the figure. Taking gravitational potential V = 0 at r = oo , the potential at the centre of the cavity thus formed is (G = gravitational constant)

From a solid sphere of mass M and radius R , a solid sphere of radius R//2 is removed as shown. Find gravitational force on mass m as shown

A particle of mass m is placed at a distance of 4R from the centre of a huge uniform sphere of mass M and radius R . A spherical cavity of diameter R is made in the sphere as shown in the figure. If the gravitational interaction potential energy of the system of mass m and the remaining sphere after making the cavity is (lambdaGMm)/(28R) . Find the value of lambda

A sphere of radius 2R and mas M has a spherical cavity of radius R as shown in the figure. Find the value of gravitational field at a point P at a distance of 6R from centre of the sphere.

A shell of mass M and radius R has point mass m placed at a distance r from its centre. The gravitational potential energy U(r) vs r will be

Three solid spheres of mass M and radius R are placed in contact as shown in figure. Find the potential energy of the system ?

A hemi-spherical cavity is created in solid sphere (of radius 2R ) as shown in the figure. Then

The figure represents a solid uniform sphere of mass M and radius R . A spherical cavity of radius r is at a distance a from the centre of the sphere. The gravitational field inside the cavity is

There is a concentric hole of radius R in a solid sphere of radius 2R. Mass of the remaining portional is M. What is the gravitational potential at centre?