Question

A stone tied to the end of a string 100 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 22 s, then the acceleration of the stone is

• A. $16ms^{- 2}$ ($16m/s^{2}$)
• B. $4ms^{- 2}$ ($4m/s^{2}$)
• C. $12ms^{- 2}$ ($12m/s^{2}$)
• D. $8ms^{- 2}$ ($8m/s^{2}$)

Answer 1

Answer: (A)

$16ms^{- 2}$ ($16m/s^{2}$)

Answer 2

Here, r = 100 cm = 1m

Frequency, $u = \frac{14}{22}Hz$

$\therefore\omega = 2\pi u = 2 \times \frac{22}{7} \times \frac{14}{22} = 4rads^{- 1}$

The accelerations of the stone is

$a_{c} = \omega^{2}r = (4)^{2}(1) = 16ms^{- 2}$