Question

A particle moves in a circular path of radius $R$. In half the period of revolution its displacement and distance covered are:

• A. $2R$, $\pi R$
• B. $R$, $\pi R$
• C. $2R$, $2\pi R$
• D. $R\sqrt{2}$, $\pi R$

Answer 1

The correct option is A $2R$, $\pi R$

$\text{Step 1: Distance Calculation}$

Let us consider that the particle starts from point A. In half revolution, the particle will be at the opposite point of diameter( at point B) covering a distance ACB(Refer Figure)

Distance in half revolution$=ACB=\frac{1}{2}$ $\text{(Circumference of circle)}$
$=\frac{2\pi R}{2}=\pi R$

$\text{Step 2: Displacement Calculation}$

Displacement is the shortest distance between the initial and final positions which is Distance $ADB$ here.

Therefore, Displacement:

$=ADB=\text{Diameter of circle}$

$=2R$

Hence A is the correct option.