If a cavity is made inside a solid sphere,the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Consider a solid sphere of uniform density $\rho$ and radius $R$. The gravitational field at any point inside a solid sphere is given by $\vec{g}

Vedclass · Accepted Answer

Uniform

Vedclass · Answer

(B) Consider a solid sphere of uniform density $\rho$ and radius $R$. The gravitational field at any point inside a solid sphere is given by $\vec{g} = -\frac{4}{3} \pi G \rho \vec{r}$,where $\vec{r}$ is the position vector from the center of the sphere.When a spherical cavity is created,the gravitational field inside the cavity is the vector sum of the field due to the original solid sphere and the field due to a smaller sphere of negative mass (representing the cavity) placed at the same location.Let $\vec{r_1}$ be the position vector from the center of the large sphere and $\vec{r_2}$ be the position vector from the center of the cavity.The total field $\vec{g}_{net} = \vec{g}_{large} + \vec{g}_{cavity} = -\frac{4}{3} \pi G \rho \vec{r_1} - (-\frac{4}{3} \pi G \rho \vec{r_2})$.Since $\vec{r_1} - \vec{r_2} = \vec{d}$,where $\vec{d}$ is the constant vector connecting the center of the sphere to the center of the cavity,we get $\vec{g}_{net} = -\frac{4}{3} \pi G \rho \vec{d}$.Since $\rho$,$G$,and $\vec{d}$ are constants,the gravitational field inside the cavity is uniform.

If a cavity is made inside a solid sphere,then the gravitational field inside the cavity is

Similar Questions

If the value of gravitational intensity at a point is $0.7\, N/kg$,what will be the magnitude of the gravitational force acting on an object of mass $5\, kg$ at that point (in $, N$)?

What is the gravitational field intensity at any point inside a uniform spherical shell?

The gravitational field,due to the 'left over part' of a uniform sphere (from which a part as shown,has been 'removed out'),at a very far off point,$P$,located as shown,would be (nearly)

Which one of the following graphs correctly represents the variation of the gravitational field $(I)$ with the distance $(r)$ from the centre of a spherical shell of mass $M$ and radius $a$?

Two concentric shells of masses $m_1$ and $m_2$ have radii $r_2$ and $r_1$ respectively (where $r_2 < r_1$). $A$ particle of mass $m$ is placed at positions $A, B,$ and $C$ as shown in the figure. The gravitational forces on the particle at these positions are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module