Solve
Guides
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Standard XII
Physics
Question

A metal sphere has radius R and mass M. A spherical hollow of diameter R is made in this sphere such that its surface passes through the centre of the metal sphere and touches the outside surface of the metal sphere. A unit mass is placed at a distance from the centre of metal sphere. The gravitational field at that point is
144413.jpg
  1. GM(R+a)2⎛⎜ ⎜ ⎜ ⎜ ⎜⎝1−18(1−R2a)2⎞⎟ ⎟ ⎟ ⎟ ⎟⎠
  2. GMa2⎛⎜ ⎜ ⎜ ⎜ ⎜⎝1−18(1−R2a)2⎞⎟ ⎟ ⎟ ⎟ ⎟⎠
  3. GM(R−a)2⎛⎜ ⎜ ⎜ ⎜ ⎜⎝1−18(1−2aR)2⎞⎟ ⎟ ⎟ ⎟ ⎟⎠
  4. GMR2⎛⎜ ⎜⎝1−18(1−2Ra)2⎞⎟ ⎟⎠

A
GM(R+a)2⎛⎜ ⎜ ⎜ ⎜ ⎜⎝1−18(1−R2a)2⎞⎟ ⎟ ⎟ ⎟ ⎟⎠
B
GMR2⎛⎜ ⎜⎝1−18(1−2Ra)2⎞⎟ ⎟⎠
C
GM(R−a)2⎛⎜ ⎜ ⎜ ⎜ ⎜⎝1−18(1−2aR)2⎞⎟ ⎟ ⎟ ⎟ ⎟⎠
D
GMa2⎛⎜ ⎜ ⎜ ⎜ ⎜⎝1−18(1−R2a)2⎞⎟ ⎟ ⎟ ⎟ ⎟⎠
Open in App
Solution
Verified by Toppr

Let ρ be the mass density.
mass of metal sphere M=ρ.43πR3
mass of hollow sphere , m=ρ.43π(R/2)3=M/8
The field at that point = field due to metal sphere − field due to hollow sphere.
f=GMa2−Gm(a−R2)2=GMa2−GM8(a−R2)2=GMa2−GM8a2(1−R2a)2=GMa2⎛⎝1−18(a−R2a)2⎞⎠

Was this answer helpful?
0
Similar Questions
Q1
A metal sphere has radius R and mass M. A spherical hollow of diameter R is made in this sphere such that its surface passes through the centre of the metal sphere and touches the outside surface of the metal sphere. A unit mass is placed at a distance from the centre of metal sphere. The gravitational field at that point is
144413.jpg
View Solution
Q2
A cavity of radius R2 is made inside a solid sphere of radius R. The centre of the cavity is located at a distance R2 from the centre of the sphere. The gravitational field intensity at a point P, as shown in the figure is:

[Here g=GMR2, where M is the mass of the solid sphere without cavity]


View Solution
Q3
A solid sphere of mass M and radius R has a spherical cavity of radius R2 such that the centre of cavity is at a distance R2 from the centre of the sphere. A point mass m is placed inside the cavity at a distance R4 from the centre of sphere. The gravitational force on mass m is
View Solution
Q4
A cavity of radius R2 is made inside a solid sphere of radius R. The centre of the cavity is located at a distance R2 from the centre of sphere . The gravitational force on a particle of mass m at a distance R2 from the centre of the sphere on the line joining both the centres of sphere and cavity is ( opposite to the centre of cavity) [ here g = GMR2 where M is the mass of the sphere].
View Solution
Q5
A activity of radius R/2 is made inside a solid sphere of radius R. The centre of cavity is located at a distance R/2 from the centre of the sphere. The gravitational force on a particle of mass ′m′ at a distance R/2 from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite to the centre of cavity). [Here g=GM/R2, where M is the mass of the sphere]
View Solution