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Mechanics

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 Joined: 3 Nov 2009 Post: 16
5 Nov 2009 21:12:45 IST
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A string ,which is 1 m long can withstand a max tension 8 kg wt. A stone of mass 0.5 kg is tied at o
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A string ,which is 1 m long can withstand a max tension 8 kg wt. A stone of mass 0.5 kg is tied at one end of the string and whirled round in a horizontal circle with a uniform angular accln .If the stone starts from rest and string breaks just when the stone has completed 100 revolusns .Find its uniform angular accln.

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Joined: 19 Feb 2009
Posts: 1979
5 Nov 2009 21:31:35 IST
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Tension in the string is due to centrifugal force which act on the mass outside at every point...

Centrifugal force is equal to mw^2r. {where m is mass,w is angular velocity,,r is radius of circle}

Now maximum tension is = 8kg

maximum tension will be equal to mw^2r....where w will be the maximum w that can be acheived by body...

So mw^2.r = 8

r=1 mass = 1.2

so w^2 = 16

hence w=4.

So maximum w corrsponding to maximum tension is 4.

Now given string breaks after 100 revolution...

so displacement is 100*2pi = 200pi {in one revolution 2pi displacement}

Now use the third equation of motion...

w{final}^2 - w{initial}^2 = 2.a.s

where a is angular acceleration and s is net displacement..

w{final} = 4

w{initial} = 0

s= 200pi

so 16 = 2.a.200pi

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Joined: 20 Apr 2008
Posts: 195
6 Nov 2009 14:38:06 IST
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Is it possible to rotate a stone tied to a string in horizontal circle? Always there will be an inclination with respect to horizontal to accommodate the force of gravity! So 'mg' also will have to be considered. In such case as we accelerate the speed of rotation the inclination will come down and stone will rise. Problem becomes complex.

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