Question

Assertion (A): The hour hand of a clock is $$6\ \text{cm}$$ long. The angle swept by it between 9.20 a.m. and 9.55 a.m. is $$35^{\circ}$$.

Reason (R): To find the area swept by the hour hand of the clock in a certain time interval, we calculate the area of the sector of a circle.

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

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

Explanation:

Step 1 – Assertion: A is false. The hour hand moves $$30^{\circ}$$ in one hour. In $$35$$ minutes, it sweeps $$30^{\circ}\times\frac{35}{60}=17.5^{\circ}$$, not $$35^{\circ}$$.

Step 2 – Reason: R is true. As the hand rotates, it sweeps out a sector of a circle, so the sector-area method applies.