Question

A particle is moving along a circular track of radius 1 m with uniform speed what is the ratio of the distance covered and the displacement in half revolution

Answer 1

Answer:  

The ratio is $\bold{\mathrm{pi} : 2}$.

Solution:

The circumference of the circular task will be the distance covered in one complete revolution.

$\bold{\text {Circumference}=\text {Distance covered in one revolution }=2 \pi r}$

Here, r is the radius of the circular track. So the distance covered in half revolution will be half of the distance covered in one complete revolution.

$\bold{\text {Distance covered in half revolution}=\frac{2 \pi r}{2}=\pi r=\pi}$

Displacement covered in one full revolution will be zero and for half revolution it will be 2r i.e., 2

So, the ratio is  

$\frac{\text { Distance }}{\text { Displacement }}=\frac{\pi}{2}$

Thus the ratio is $\bold{\mathrm{pi} : 2}$.