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10 May 2009 09:28:44 IST
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Respected Expert , I have posted six times this questions but no answer. Plz give me solution.Two small sphere having mass 10 kg each are kept i meter apart on smooth surface . After what time they will be united due to gravitational force . Ans is 14.3 days .
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10 May 2009 20:15:14 IST
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Let at any instant of time the seperation between them is x. The gravitational force on one sphere due to the other is F = Gm^2 / x^2. the acceleration of this sphere is a = F/m. Similarly the other sphere will have acceleration a in the opposite direction. Hence acceleration with which they approach is 2a. 2a = v dv/dx. hence find velocity as function of x. then find time by putting v = dx/dt
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10 May 2009 20:28:29 IST
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Calculate the force between the two spheres using F = GMm/r^2 After calculating the force, now u can find out the acceleration using a = F/M. Now use eq. of motion S = ut + (1/2)at^2 and calculate the time (remember u = 0).
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10 May 2009 21:07:36 IST
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deepak, r is not constant, hence one cannot use equations of motion as they are valid for constant acceleration. Hence integration is required
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10 May 2009 21:10:22 IST
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very easy qs just sit on one sphere apply the virtual force to other and use simple integration...........
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10 May 2009 21:12:01 IST
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der comes the problem...........after doing integration and putting the limits.we get 1/0.........indeterminate
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10 May 2009 21:18:16 IST
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after sitting on one block the acc. of other is 2a. where a = Gm/R^2 so A = 2GM/r^2 i.e.  now take r^2 one side and it becomes 
now do double integration and see the boundary condition.
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WALK NOT AS IF YOU RULE THE WORLD...
BUT AS IF YOU DON'T CARE WHO RULES IT....
MAN WOULD DO NOTHING IF HE WAITED UNTIL HE COULD DO IT SO WELL THAT NO OTHER BEING CAN FIND FAULT WITH IT..................NEWMAN
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10 May 2009 21:23:17 IST
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okay integral rsquare dr=-(1/r)........right......................then putting da limits(r varies from R to 0)....................u will get(1/R- 1/0)
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10 May 2009 21:28:49 IST
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theres no such thing as a double integration... use my method, integrate and find v as a function of x(or r) then put v = dx/dt and again integrate under the proper limits
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10 May 2009 23:57:58 IST
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@ady just coz U don't know it doesn't mean it doesn't exist!! Double integration does exist, and is taught by many IIT-JEE coaching institutes!! Infact even triple, quadruple and so on integrals do exist.....this U will learn first yr of engineering!! http://en.wikipedia.org/wiki/Multiple_integral
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10 May 2009 23:59:55 IST
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Yeah man, think twice before saying that it does NOT exist.
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11 May 2009 07:44:54 IST
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k, guys , sorry about that
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