Question

A car is taking a circular turn of radius 90 m with a constant speed of 15 m/s. The radial acceleration of the car is:
1. 0 m/s²
2. 2.5 m/s²
3. 25 m/s²
4. 5 m/s²

Answer 1

Correct Answer - Option 2 : 2.5 m/s²

CONCEPT:

Circular motion:

• The motion of a body moving around a fixed point in a circular path is known as circular motion.
• Example:
  1. The motion of the moon around the earth.
  2. The motion of a satellite around its planet.
• The direction of motion changes continuously in a circular motion, therefore the circular motion is an accelerated motion.

Uniform circular motion:

• If the angular velocity of the body remains constant during circular motion then it is called uniform circular motion.
• Uniform circular motion is an accelerated motion because the direction of motion of the body continuously changes.

Non-Uniform circular motion:

• If the angular velocity of the body changes during circular motion then it is called non-uniform circular motion.

CALCULATION:

Given R = 90 m, and v = 15 m/s

• Since the speed is constant during the circular motion so it is a case of uniform circular motion.
• We know that in a uniform circular motion the radial acceleration is given as,

\(⇒ a_r=\frac{v^2}{R}\)     -----(1)

Where a_r = radial acceleration, v = speed and R = radius of circular motion

By equation 1,

\(⇒ a_r=\frac{15^2}{90}\)

⇒ a_r = 2.5 m/s²

• Hence, option 2 is correct.