Question

A rod of length $10\text{m}$ is placed in vertical direction. Then the rod is rotated by ${90}^{\circ }$ in clockwise direction. Find out the displacement of the $COM$ of the rod.

• A. $5\sqrt{2}\text{m}$
• B. $\frac{5}{\sqrt{2}}\text{m}$
• C. $5\text{m}$
• D. $2\sqrt{5}\text{m}$

Answer 1

The correct option is A $5\sqrt{2}\text{m}$


When rod $AB$ rotates ${90}^{\circ }$ in clockwise direction, it becomes horizontal.
$COM$ of rod before rotation
$(x_1,y_1)=(0,5)\text{m}$
$COM$ of rod after rotating ${90}^{\circ }$ in clockwise direction
$(x_2,y_2)=(5,0)\text{m}$
The displacement of the $COM$ of the rod is $r$
$r=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
$=\sqrt{(5-0{)}^2+(0-5{)}^2}=5\sqrt{2}\text{m}$
$\therefore r=5\sqrt{2}\text{m}$