Integration problem

Question

Answer 1

Step 1:

Force of attraction :

The force of gravitational attraction is proportional to the product of the masses ( and ) and is inversely proportional to the square of the distance between the two masses, r.

Inversely proportional means that the attraction is strong when the masses are close to each other, and weak when the masses are far away from each other.

The formula for the force of gravitational attraction is : .

Where is the gravitational constant.

is the distance from mass to one end of rod end of mass .

is the distance from mass to another end of rod end of mass .

Step 2:

Find the force of attraction of a material rod.

The length of the rod is .

The mass of the rod .

On a material point of mass lying on a straight line with the rod at a distance from one of its ends.

Draw a diagram for the given information :

Observe the diagram :

and .

Force of attraction of a material rod .

Since the two masses lying on the straight line with same direction, take .

Substitute and in .

.

Force of attraction of a material rod is , Where is the gravitational constant.

Solution:

Force of attraction of a material rod is , Where is the gravitational constant