A solid sphere of uniform density and radius 4 units is located w… - Vidyadip

MCQ

A solid sphere of uniform density and radius 4 units is located with its centre at the origin $O$ of coordinates. Two spheres of equal radii $1$ unit with their centres at $A(-2,0,0)$ and $B(2,0,0)$ respectively are taken out of the solid leaving behind spherical cavities as shown in figure

A
The gravitational force due to this object at the origin is zero
B
The gravitational potential is the same at all points on the circle $y^2+z^2=4$
C
The gravitational potential is the same at all points of the circle $y^2+z^2=36$
✓
All of the above.

✓

Answer

Correct option: D.

All of the above.

Since cavities are symmetrical w.r.t. O. So the gravitational force at the centre is zero.The radius of the circle $z^2+y^2=36$ is $6.$
For all points for $r \geq 6$, the body behaves as if whole of the mass is concentrated at the centre.
So the gravitational potential is same.Above is true for $z^2+y^2=4$ as well.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Gravitation→Gravitation — all question types→JEE physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Plane of eddy currents makes an angle with the plane of magnetic lines of force equal to

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by $100 \mathrm{~Hz}$, then the fundamental frequency of open pipe is:

In a thermodynamics process, pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20 \mathrm{~J}$ of heat and 8J of work is done on the gas. If the initial internal energy of the gas was $30 \%$. The final internal energy will be

The absolute temperatures of two black bodies are $2000 K$ and $3000 K$ respectively. The ratio of wavelengths corresponding to maximum emission of radiation by them will be

A galvanometer gives full scale deflection with $0.006$ A current. By connecting it to a $4990 \ \Omega$ resistance, it can be converted into a voltmeter of range $0-30 \ V$. If connected to a $\frac{2 n }{249} \Omega$ resistance, it becomes an ammeter of range $0-1.5 \ A$. The value of $n$ is:

If the Young's modulus of the material is 3 times its modulus of rigidity, then its volume elasticity will be

An image of the sun is formed by a lens of focal length of $30 \mathrm{~cm}$ on the metal surface of a photoelectric cell and a photoelectric current $I$ is produced. The lens forming the image is then replaced by another of the same diameter but of focal length $15 \mathrm{~cm}$. The photoelectric current in this case is

The current conduction in a discharged tube is due to

An engine is supposed to operate between two reservoirs at temperature $727^{\circ} \mathrm{C}$ and $227^{\circ} \mathrm{C}$. The maximum possible efficiency of such an engine is

The plots of intensity versus wavelength for three black bodies at temperatures $T, T$ and $T$ respectively are as shown. Their temperature are such that