Question

Figure 13-25 shows three situations involving a point particle P with mass m and a spherical shell with a uniformly distributed mass M. The radii of the shells are given. Rank the situations accordingto the magnitude of the gravitational force on particle P due to the shell, greatest first.

Short answer

The order of the situations according to the gravitational force on the particle P due to shell is b = c > a.

Step-by-step solution

The given data

The figure for particle-shell system

Understanding the concept of the gravitational force

The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them, according to Newton's universal law of gravitation.Using the formula for the gravitational force of attraction, we can determine the ranking of the situations according to the magnitude of the gravitational force on P due to the spherical shell.

Formula:

The Gravitational force of attraction between two bodies of masses M and m separated by distance R is, $F=\frac{GMm}{R^2}$ …(i)

Calculation of the order of the situations according to the force

In situation b) and c), the distance between particle P and spherical shell which acts as a point mass concentrated at its center is d .

So, the Gravitational force of attraction between the particle P of mass d and a spherical shell of mass M separated by distance d is can be given using equation (i) as:

$F=\frac{GMm}{d^2}$

In situation a) the particle P is inside the spherical shell which acts as a point mass concentrated at its center. So, the spherical shell exerts no force on it.

Therefore, the order of the situations according to the gravitational force on the particle P due to shell is b = c > a.