Question

The minute hand of a clock is 5cm long. Calculate the linear speed of an ant sitting at the tip

Answer 1

Answer:

0.52 cm/min

Explanation:

angular speed =

2π/(60)

linear speed = 5 X angular speed

Answer 2

The linear speed of an ant sitting at the tip of the 5 cm long minute hand is 8.7 × 10⁻⁵ m/s.

Given,

The minute hand of a clock is 5 cm long.

An ant is sitting at its tip.

To find,

The linear speed of ant.

Solution,

It can be seen that here, the length of the minute hand of a clock is given to be 5 cm.

We know that, for a body moving along a circular path about a fixed point, the relationship between linear speed and angular speed is given as

$v=r \omega \hfill ...(1)$

where,

v = linear speed,

r = radius of the circle (or distance of the body from the fixed point),

ω = angular speed.

So, here, we first need to find the angular speed of the minute hand.

We know that the minute hand returns to its initial position, or completes one revolution, in 1 hour.

∵ 1 h = 60 min = 3600 s.

We can say,

in 3600 s, angle turned = $2\pi$.

So, in 1 s

$=\frac{2\pi }{3600} \\= \frac{\pi}{1800}$

= 1.74 × 10⁻³ rad/s.

This will be the angular speed of the minute hand, that is, 1.74 × 10⁻³ rad/s.

Here,

r will be taken as 5 cm = 5 × 10⁻² m.

Thus, using (1), the linear speed of the ant,

$v=5 \times 10^{-2} \times 1.74 \times 10^{-3}$

$\implies v=8.7 \times 10^{-5}$ m/s.

Therefore, the linear speed of an ant sitting at the tip of the 5 cm long minute hand is 8.7 × 10⁻⁵ m/s.

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