A stone of mass m at the end of a string
of length l is whirled in a vertical circle at a constant speed. What position
of the stone shall result in the maximum tension in the string?
लंबाई l की एक स्ट्रिंग के अंत में m द्रव्यमान का एक पत्थर एक स्थिर गति से एक ऊर्ध्वाधर वृत्त में घुमाया जाता है। पत्थर की किस स्थिति के परिणामस्वरूप डोरी में अधिकतम तनाव होगा?
Quarterway down from the top
Half way down from the top
At the bottom of the circle
At the top way of the circle
At the bottom of the circle
Let v be the velocity of rotation of
the stone (where 
)
Considering various conditions at
dynamic equilibrium of the rotating stone
Tension on the string at position 1,
Similarly, at position 2,
At position 3,
At position 4,
Therefore, T1>(T2= T4)>T3
Tension will be maximum at the bottom
of the circle i.e.,
Hence, the correct option is (C).
&Key Points:-
The value of tension can also be calculated using the expression
Where, T = Tension in the string,
m = Mass of the stone
i = Radius of rotation or
length of the string
0 = Angular position (take
position 1 as reference i.e.,0 = 00 ).
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