Question

Write the expression for censor mass of a uniform rod

Answer 1



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Class 11

Physics

System of Particles and Rotational Motion

Centre of mass of a Uniform Rod

1

7265

Suppose a rod of mass M and length L is lying along the x-axis with its one end at x = 0 and the other at x = L.

Mass per unit length of the rod l = M/L

Hence, dm, (the mass of the element dx situated at x = x is) = l dx
The coordinates of the element dx are (x, 0, 0). Therefore, x-coordinate of COM of the rod will be





The y-coordinate of COM is


Similarly, zCOM = 0

i.e., the coordinates of COM of the rod are ( 0, 0), i.e., it lies at the centre of the rod.

Answer 2

hyy mates

Suppose a rod of mass M and length L is lying along the x-axis with its one end at x = 0 and the other at x = L.

Self Study Point

Home Class 11

Class 11PhysicsSystem of Particles and Rotational Motion

Centre of mass of a Uniform Rod

17265

Suppose a rod of mass M and length L is lying along the x-axis with its one end at x = 0 and the other at x = L.

Mass per unit length of the rod l = M/L

Hence, dm, (the mass of the element dx situated at x = x is) = l dx

The coordinates of the element dx are (x, 0, 0). Therefore, x-coordinate of COM of the rod will be

The y-coordinate of COM is

Similarly, zCOM = 0

i.e., the coordinates of COM of the rod are ( 0, 0), i.e., it lies at the centre of the rod.