Question 43: Work, Energy and Power & Circular Motion

Question

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

Accepted Answer

To determine the distance traveled by the tips of the second hand and the minute hand, we need to calculate the circumference of the circles they make. Let's start by calculating the distances traveled by both hands over a period of 30 minutes.
First, the circumference formula is given by:
$$C = 2\pi r$$
For the second hand:
The length of the second hand is $$75 \space 	ext{cm}$$. The second hand completes one full revolution every 60 seconds, so in 1 minute, the second hand travels:
$$ 	ext{Distance per minute} = 2\pi 	imes 75 	ext{ cm} $$
In 30 minutes, the second hand will travel:
$$ 	ext{Total distance traveled by second hand} = 30 	imes 2\pi 	imes 75 	ext{ cm} $$
Now, let's calculate it with $$\pi = 3.14$$:
$$ 	ext{Total distance traveled by second hand} = 30 	imes 2 	imes 3.14 	imes 75 	ext{ cm} $$
$$ 	ext{Total distance traveled by second hand} = 30 	imes 471 	ext{ cm} = 14130 	ext{ cm} $$
For the minute hand:
The length of the minute hand is $$60 	ext{ cm}$$. The minute hand completes one full revolution every 60 minutes, so in 30 minutes, the minute hand travels:
$$ 	ext{Total distance traveled by minute hand} = 0.5 	imes 2\pi 	imes 60 	ext{ cm} $$
Again, let's calculate it with $$\pi = 3.14$$:
$$ 	ext{Total distance traveled by minute hand} = 0.5 	imes 2 	imes 3.14 	imes 60 	ext{ cm} $$
$$ 	ext{Total distance traveled by minute hand} = 0.5 	imes 376.8 	ext{ cm} = 188.4 	ext{ cm} $$
The difference in distance $$x$$ is:
$$ x = 14130 	ext{ cm} - 1884 	ext{ cm} $$
$$ x = 13941.6 	ext{ cm} $$
Convert this distance into meters:
$$ x = 13941.6 	ext{ cm} 	imes \frac{1 	ext{ meter}}{100 	ext{ cm}} $$
$$ x \approx 139.4 	ext{ meters} $$
Thus, the value of $$x$$ in meters is nearly 139.4 meters, making the correct option:
Option C

Answer

118.9

Answer

140.5

Answer

139.4

Answer

220.0

Work, Energy and Power & Circular Motion

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

Choose the correct answer: