A stone of mass m tied to the end of a string, is whirled around in a horizontal circle. (Neglect the force due to gravity). The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by `T = Ar^2` where A is a constant, r is the instantaneous radius fo the circle and n=....
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Let at any instant of time t, the radius of the horizontal surface be r. `T = mromega^2 …(i)` Where m is the mass of stone and `omega` is the angular velocity at that instant of time t. Also, L = I omega ….(ii)` From (i) and (ii)` `T = (mrL^2)/(I^2) = (mL^2)/((mr^2))^2 xxr , T =((L^2)/(m)) r^(-3)` `=Ar(-3) (where (L^2)/(m) = A is constant)` Thus, =3. ` (##JMA_RM_C06_004_S01.png" width="80%">
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