Question

A clock has a 75 cm long second hand and a 60 cm long minute hand, respectively. In 30 minutes duration, the tip of the second hand will travel $x$ distance more than the tip of the minute hand. The value of $x$ in meters is nearly (Take $\pi = 3.14$):

• A. 139.4
• B. 140.5
• C. 220.0
• D. 118.9

Answer 1

The Correct Option is A

The distance traveled by the tip of the minute hand in one revolution is:
$x_{\text{min}} = \pi \times r_{\text{min}} = \pi \times \frac{60}{100} \, \text{m}.$
$x_{\text{min}} = 3.14 \times 0.6 = 1.884 \, \text{m}.$

The distance traveled by the tip of the second hand in 30 minutes is:
$x_{\text{second}} = 30 \times 2\pi \times r_{\text{second}}$
$x_{\text{second}} = 30 \times 2 \times 3.14 \times \frac{75}{100} \, \text{m}.$
$x_{\text{second}} = 30 \times 4.71 = 141.3 \, \text{m}.$

The difference in distance is:
$x = x_{\text{second}} - x_{\text{min}} = 141.3 - 1.884 \, \text{m}.$
$x = 139.4 \, \text{m}.$

Final Answer: 139.4 m.