why we can't assume the whole mass of a rod at its center of mass while finding the gravitational force between the uniform rod and a point mass.
Answer (1)
13th Jan, 2021
Dear student,
A uniform rod has the mass distributed all over it's volume. Means the rod is an example of uniform mass distribution.
But the according to newton the gravitational force formula is applied or used for point masses.
So, if you wasn't to find the gravitational force between a point mass and a rod of uniform mass, so first take an elemental strip of a small mass on rod ( such that it acts like a point mass ). Now, find the gravitational force between that element and the given point mass.
And then integrate it over the whole length.
A uniform rod has the mass distributed all over it's volume. Means the rod is an example of uniform mass distribution.
But the according to newton the gravitational force formula is applied or used for point masses.
So, if you wasn't to find the gravitational force between a point mass and a rod of uniform mass, so first take an elemental strip of a small mass on rod ( such that it acts like a point mass ). Now, find the gravitational force between that element and the given point mass.
And then integrate it over the whole length.
2 Comments
Comments (2)
My question is why wouldn't we take the centre of mass of rod for the calculation of gravitation force because COM as also act as point mass and then Newton low of gravitation is valid
Reply
13th Jan, 2021
Rahul upadhyay
Yes, I understand and I have given answer as per your question.
For the rod, the mass is distributed all over its entirety. And center of mass is not real thing. It is an imagination. Center of mass is an imaginary point where the whole mass of system is assumed. But for newton gravitation formula, it cannot be used because the formula is used for a point mass. And the uniform rod has a uniform mass distribution. And thus you cannot imagine or assume the whole mass to be concentrated at it's centre of mass while using the gravitational force formula.
Also remember the concept of moment of inertia in rotation, where you have derived the moment of inertia for a rod. At that time too, you didn't assumed the whole mass at center of instead during the derivation of moment of inertia from the mid point of rod, you have integrated it from -l/2 to +l/2.
For the rod, the mass is distributed all over its entirety. And center of mass is not real thing. It is an imagination. Center of mass is an imaginary point where the whole mass of system is assumed. But for newton gravitation formula, it cannot be used because the formula is used for a point mass. And the uniform rod has a uniform mass distribution. And thus you cannot imagine or assume the whole mass to be concentrated at it's centre of mass while using the gravitational force formula.
Also remember the concept of moment of inertia in rotation, where you have derived the moment of inertia for a rod. At that time too, you didn't assumed the whole mass at center of instead during the derivation of moment of inertia from the mid point of rod, you have integrated it from -l/2 to +l/2.
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