Question

A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed if the stone makes 14 revolutions in 25 seconds what is the magnitude of acceleration of the stone

Answer 1

A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed if the stone makes 14 revolutions in 25 seconds what is the magnitude of acceleration of the stone

Answer 2

Length of the string, l = 80 cm = 0.8 m

Number of revolutions = 14

Time taken = 25 s

Frequency, v = Number of revolutions / Time taken  =  14 / 25 Hz

Angular frequency, ω = 2πν

= 2 × (22/7) × (14/25)  =  88 / 25 rad s-1

Centripetal acceleration, ac = ω2r

= (88/25)2 × 0.8

= 9.91 ms-2

The direction of centripetal acceleration is always directed along the string, toward the centre, at all points.