Question

A rod of length $10\text{m}$ is inclined on the wall at an angle ${37}^{\circ }$ with horizontal.


Find out position of centre of mass of the rod assuming the wall to be along $y-$ axis and foot of the wall as the origin.

• A. $(5\text{m},4\text{m})$
• B. $(4\text{m},5\text{m})$
• C. $(5\text{m},3\text{m})$
• D. $(4\text{m},3\text{m})$

Answer 1

The correct option is D $(4\text{m},3\text{m})$

Co-ordinates of $COM$ of uniform rod is at the distance of $\frac{l}{2}$ from its either end.


Foot of the wall is considered as origin (Given)
Then, $x-$ co-ordinate of $COM$ of rod is $\frac{l}{2}\cos \theta$ $=\frac{10}{2}\times \cos {37}^{\circ }=5\times \frac{4}{5}=4\text{m}$
ands $y-$ co-ordinate of $COM$ of rod is $\frac{l}{2}\sin \theta$ $=\frac{10}{2}\times \sin {37}^{\circ }=5\times \frac{3}{5}=3\text{m}$
Therefore,
co-ordinates of $COM$ are $(4\text{m},3\text{m})$