Question 210: Work, Energy and Power & Circular Motion

Question

A particle performing uniform circular motion of radius $\frac{\pi}{2} \mathrm{~m}$ makes $x$ revolutions in time $t$. Its tangential velocity is

Accepted Answer

Step 1: Write the formula for tangential velocity.
The tangential velocity $v$ for a particle in uniform circular motion is given by:
$$ v = \frac{	ext{distance travelled}}{	ext{time}} $$
Step 2: Find the distance travelled in $x$ revolutions.
In 1 revolution, distance = circumference of circle $= 2\pi r$
For $x$ revolutions, distance $= x 	imes 2\pi r$
The radius is given as $r = \frac{\pi}{2}\ 	ext{m}$.
So,
$$ 	ext{distance} = x 	imes 2\pi \left(\frac{\pi}{2}ight) $$
$$ 	ext{distance} = x 	imes \pi 	imes \pi = x\pi^2 $$
Step 3: Divide total distance by total time.
Total time taken $= t$
$$ v = \frac{x\pi^2}{t} $$
Step 4: Match with the given options.
Option C
$\boxed{\frac{\pi^2 x}{t}}$
This is the correct answer.

Answer

$\frac{x}{\pi t}$

Answer

$\frac{\pi^2}{x t}$

Answer

$\frac{\pi^2 x}{t}$

Answer

$\frac{\pi x}{t}$

Work, Energy and Power & Circular Motion

A particle performing uniform circular motion of radius \frac{\pi}{2} \mathrm{~m} makes x revolutions in time t. Its tangential velocity is

Choose the correct answer: