Question

A minute hand a clock is 8cm long. Calculate the linear speed of ant sitting at its tip

Answer 1

here, angular velocity of minute is

  ω= 2π/3600 rad sec⁻¹

as minute hand covers 2π radian in 1 hour

 length if minute hand = r

now linear velocity v is given  by,

  v = rω

∴v = 0.08 × 2π/3600 = 0.08 × π/1800 = 8π/180000 m sec⁻¹

Answer 2

Given :

Length of minute hand , l = 8 cm = 0.08 m .

To Find :

The linear speed of ant sitting at its tip .

Solution :

Angular velocity of minute clock is :

Time taken by minute hand to reach the starting point :

$T=60\times 60\ s =3600\ s$

Angular velocity is given by :

$\omega=\dfrac{2\pi}{T}\\\\\omega=\dfrac{2\times 3.14}{3600}\ rad/s\\\\\omega=1.74\times 10^{-3}\ rad/s$

Now , linear speed at tip is given by :

$v=\omega L\\\\v=1.74\times 10^{-3}\times 0.08\ m/s\\\\v=1.39\times 10^{-4}\ m/s$

The linear speed of ant sitting at its tip is $1.39\times 10^{-4}\ m/s$ .

Hence , this is the required solution .