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Question

A stone tied to the end of a string of length 1 m is whirled in a horizontal circle with a constant speed. If stone makes 22 revolution in 44 second, what is the magnitude and direction of the acceleration of stone?

A
Acceleration will be π2 m/s2 radially inwards.
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B
Acceleration will be π2 m/s2 radially outwards.
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C
Acceleration will be π2 m/s2 along the tangent to the circle.
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D
Acceleration will be π4 m/s2 radially inwards.
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Solution

The correct option is A Acceleration will be π2 m/s2 radially inwards.
Radial acceleration or centripetal accceleration is given by:
ac=v2r=ω2r
Frequency of revolution is,
f=2244=12 s1
ω=2πf=π rad/s
ac=ω2r=π2×1=π2 m/s2


Tangential acceleration is the rate of change of speed w.r.t time:
at=dvdt=0
speed is constant
Hence net acceleration of stone a given by:
a=ac+at=ac=π2 m/s2
|a|=|ac|=π2 m/s2
Direction is along the radius towards the centre i.e. radially inwards.

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