Question

A uniform rod of length $1.0$ metre is bent at its midpoint to make ${90}^{}$ angle. The distance of the centre of mass from the centre of the rod is

• A. $35.3cm$
• B. $25.2cm$
• C. $17.7cm$
• D. zero

Answer 1

The correct option is A $35.3cm$

Given,

Length of rod, $L=1m$

Let the mass of the rod be $2m$.

When the rod is bent, the length of each part is L/2.

So, coordinates on x-axis, $(x_1,y_1)=(L/2,0)$

Coordinates on y-axis, $(x_2,y_2)=(0,L/2)$

The centre of mass of both parts from the bent corner is:

$x_{COM}=\frac{m_1{x}_1+m_2{x}_2}{m_1+m_2}$

$=\frac{m\left(\frac{L}{2}\right)+m\left(0\right)}{2m}$

$=\frac{L}{4}$

$y_{COM}=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}$

$=\frac{m\left(0\right)+m\left(L/2\right)}{2m}$

$=\frac{L}{4}$

So, centre of mass is $(L/4,L/4)$

Distance from corner is,

$d=\sqrt{{\left(\frac{L}{4}\right)}^2+{\left(\frac{L}{4}\right)}^2}$

$d=\frac{L}{4}\sqrt{2}$

$d=\frac{1}{2\sqrt{2}}$

$d=0.353m$

$d=35.3cm$