Centre Of Mass

Classical Mechanics Level 3

A train of mass M = π kg M=\pi \text{ kg} is moving on a circular track of radius R R with constant speed V = 2 ms − 1 V=2 \text{ ms}^{-1} . The length of train is half the perimeter of the track. Find the linear momentum of the train.


The answer is 4.

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Akshat Sharda by Akshat Sharda , 21, India

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3 solutions

Steven Chase
Aug 28, 2016

7 Helpful 1 Interesting 1 Brilliant 0 Confused
Joe Mansley
Jul 7, 2019

The distance between the two ends of the train is 2, the speed is 2, the mass is pi, and the length is pi. So the momentum is pi/pi 2 2=4.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Prakhar Bindal
Aug 31, 2016

On bit of observation vertical velocities will cancel up .

Consider a small element at an angle x .

Its momentum (in horizontal direction) = dm * vsin(x)

dm = (M/pi*R)(Rdx)

Integrate from 0 to pi to get 2Mv/pi

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