Question

Assertion (A): If a bicycle wheel makes $$5000$$ revolutions in moving $$11\ \text{km}$$ then the diameter of the wheel is $$70\ \text{cm}$$.

Reason (R): The distance covered by a wheel in $$1$$ revolution is equal to the circumference of the wheel.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (А).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:

Step 1 – Assertion: A is true. The distance covered in one revolution is $$\frac{11\times1000}{5000}\ \text{m} = 2.2\ \text{m} = 220\ \text{cm}$$. Thus $$\pi d = 220\ \text{cm}$$ and using $$\pi = \frac{22}{7}$$ gives $$d = 70\ \text{cm}$$.

Step 2 – Reason: R is true. In one complete revolution, the wheel travels a distance equal to its circumference.

Step 3 – Link: The reason equates the distance per revolution to the wheel’s circumference, which is the key step used to establish the asserted diameter.