Question

A student runs along a circular track of diameter \(80\) m. The distance travelled and the magnitude of displacement of the student when he covers \(\left(\frac{3}{4}\right)^{th}\) of the circle is (in m)

• A. \(60\pi ,40\sqrt{2}\)
• B. \(40\pi ,60\sqrt{2}\)
• C. \(120\pi ,80\sqrt{2}\)
• D. \(80\pi ,120\sqrt{2}\)

Hint:

Distance is the arc length covered, while displacement is the straight chord joining the start and end points.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Distance is the length of the path travelled. Displacement is the straight line from the start point to the end point.

Step 2: Distance
Radius \(R=40\) m. One full circle is \(2\pi R=80\pi\) m.
For three quarters, distance \(=\dfrac{3}{4}\times80\pi=60\pi\) m.

Step 3: Displacement
After \(270^{\circ}\) the student and the start point are joined by a chord.
The chord of a quarter circle position is the hypotenuse of a right triangle with sides \(R\) and \(R\), so displacement \(=\sqrt{2}R=40\sqrt{2}\) m.

Step 4: Compare the options
This matches option (A).

Final Answer:
The distance is 60 pi m and the displacement is 40 root 2 m. \[ \boxed{\text{(A) }60\pi,\ 40\sqrt{2}} \]