Two identical heavy spheres are separated by a distance 10 times their radius. Will an object placed at the midpoint of the line joining their centres be in stable equilibrium or unstable equilibrium? Give reason for your answer.
Two identical heavy spheres are separated by a distance 10 times their radius. Will an object placed at the midpoint of the line joining their centres be in stable equilibrium or unstable equilibrium? Give reason for your answer.
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1 Answer
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This is a Short Answer Type Questions as classified in NCERT Exemplar
Explanation- Let M be the mass and R be the radius of sphere . an object of mass m be placed at the mid point P of the line joining their centres
Force F1=F2=GMm/ (5R)2
If we displace it through x distance
New force towards sphere A, F1'= GMm/ (5R-x)2
Sphere B F2' = GMm/ (5R+x)2
As F1'>F2' therefore a resultant force (F1'-F2') acts on the objects towards sphere A therefore objects start to move towards A hence equilibrium is unstable.
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->R3 = (R + x)2 (R – x)
->R3 = (R2– x2) (R + x)
->x2 + Rx – R2 = 0
Stress
R is not correct.
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