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Q. 7

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 353

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Short Answer

A sphere is at the origin and a sphere is at At what position on the x-axis could you place a small mass such that the net gravitational force on it due to the spheres is zero?

At the position of a small mass could be placed, such that the net gravitational force on it due to the spheres is zero.

See the step by step solution

Step by Step Solution

Step 1 : Given information.

Mass of the sphere at origin (m) = mass of the sphere at

Step 2 : Calculation.

The formula to be used is :

Where and are masses, is the distance between the centre of the masses and is the universal gravitational constant.

Step 3 : Continuation of calculation.

Let the position of the small mass be and mass is Hence the force on the small mass due to is :

And force due to is :

The total force on the small mass will be zero if the above two forces are equal and opposite.

So, equate the above two forces and solve for

Step 4 : Continuation of calculation.

Comparing we get,

The above two solutions show at which position forces will be equal.

Now, since the both forces are attractive forces, they will be opposite only when the small mass is in between the two masses.

Hence, the correct answer is

Step 5 : Final answer.

At the position of a small mass could be placed, such that the net gravitational force on it due to the spheres is zero.

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