A scooter is going round a circular road of radius 100 m at a speed of 10 m/s. The angular speed of the scooter will be

The correct option is 0.1 rad/s.

Understanding the concepts:
When an object moves in a circular path, its linear speed is directly related to its angular speed. Linear speed describes how fast the object travels along the circumference, while angular speed represents the rate at which the angle changes at the center of the circle.

The formula relating linear speed, radius, and angular speed is:

$v=r\omega$

Where:
$v$
is the linear speed,
$r$
is the radius of the circular road, and
$\omega$
is the angular speed.

Rearranging the formula to solve for the angular speed:

$\omega =\frac{v}{r}$

Given values:
Radius of the circular road,
$r=100\text{m}$
Linear speed of the scooter,
$v=10\text{m/s}$

Step-by-step Calculation:
Substitute the given values into the rearranged equation:

$\omega =\frac{10}{100}$

Simplify the fraction to find the angular speed:

$\omega =0.1\text{rad/s}$

Therefore, the angular speed of the scooter is 0.1 rad/s.