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Integration problem

0 votes

asked Jul 6, 2015 in CALCULUS by anonymous
reshown Jul 6, 2015 by casacop

1 Answer

0 votes

Step 1:

Force of attraction :

The force of gravitational attraction is proportional to the product of the masses (image and image) 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 : image.

Where image is the gravitational constant.

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

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

Step 2:

Find the force of attraction of a material rod.

The length of the rod is .

The mass of the rod image.

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

Draw a diagram for the given information :

image

Observe the diagram :

image and image.

Force of attraction of a material rod image.

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

Substitute image and image in image.

image.

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

Solution:

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

answered Jul 6, 2015 by lilly Expert

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