Question

A body is travelling in a circle of radius $10\text{cm}$ as shown. Which of the following statements are true when the body reaches $\text{N}$ from $\text{M}$ along the circumference of the circle in $1\text{min}$?

• A. The distance covered by the body $=5\pi \text{cm}$
• B. The displacement of the body $=10\sqrt{2}\text{cm}$
• C. The average speed of the body $=\frac{\pi }{12}\text{cm}{\text{s}}^{-1}$
• D. The average velocity of the body $=\frac{1}{3\sqrt{2}}\text{cm}{\text{s}}^{-1}$

Answer 1

Answer: (A), (B), (C), (D)

The average velocity of the body $=\frac{1}{3\sqrt{2}}\text{cm}{\text{s}}^{-1}$

Given:
The radius of the circular path, $r=10\text{cm}$
$⟹$ The circumference of the path, $C=2\pi r=20\pi \text{cm}$
The distance travelled by the body from $\text{M}$ to $\text{N}$, $d=\frac{1}{4}\times C=\frac{20\pi }{4}=5\pi \text{cm}$


The displacement from $\text{M}$ to $\text{N}$ is the straight line joining them. The length of $\text{MN}$, according to the Pythagoras theorem, would be:
$\text{MN}=D=\sqrt{(10{)}^2+(10{)}^2}$
$=10\sqrt{2}\text{cm}$
Also, the time taken to reach $\text{N}$ from $\text{M}$, $t_{\text{MN}}=1\text{min}=60\text{s}$.
Average speed
$=\frac{d}{t_{\text{MN}}}=\frac{5\pi }{60}=\frac{\pi }{12}\text{cm}{\text{s}}^{-1}$
Average velocity
$=\frac{D}{t_{\text{MN}}}=\frac{10\sqrt{2}}{60}=\frac{\sqrt{2}}{6}=\frac{\sqrt{2}}{3\times 2}$

$=\frac{1}{3\sqrt{2}}\text{cm}{\text{s}}^{-1}$