Question

A metre stick is placed vertically at the origin on a frictionless
surface. A gentle push in +x-direction is given to the top
most point of the rod, when it has fallen completely
x-coordinate of centre of rod is at
(a) origin (b) – 0.5 m (C) -1m (d) +0.5 m​

Answer 1

Given : A metre stick is placed vertically at the origin on a frictionless surface. A gentle push in +x-direction is given to the topmost point of the rod.

To find : when it has fallen completely, x - coordinate of centre of mass of rod.

solution : Read the statement sincerely, “ A gentle push in +x-direction is given to the top

A gentle push in +x-direction is given to the topmost point of the rod.”

it seems there is no external force applied on the rod along x - axis .

but we know, if external force acting on the particle is zero, position of centre of mass remains same. it doesn't change.

so, new x - coordinate of centre of mass of rod = initial x - coordinate of centre of mass of rod

we have initial centre of mass = (0, 0.5)

i.e., initial x - coordinate of com = 0

so, new x - coordinate of com = 0

but y - coordinate has changed, because an gravitational force acting along y - axis. and it will be changed from 0.5 to zero as shown in figure.

x = 0, and y = 0 i.e., origin

Therefore new centre of mass of rod at origin.

option (a) is correct choice.