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.