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### Motion in a plane NCERT Solutions Class 11 Physics - Solved Exercise Question 4.17

Question 4.17:

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 s, what is the magnitude and direction of acceleration of the stone ?

Solution:

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 X (22/7) X (14/25)  =  88 / 25 rad s-1
Centripetal acceleration, ac = ω2r
= (88/25)2 X 0.8
= 9.91 ms-2
The direction of centripetal acceleration is always directed along the string, toward the centre, at all points.
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