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  • 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 a 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 a reason for your answer.

Answers (1)

m_{1}=m_{2}=M

r=10\; R

mass Let m be placed at the midpoint P of the line joining centres of spheres A and B

\left | F_{2} \right |=\left | F_{1} \right |=\frac{GMm}{(5R)^{2}}=\frac{GMm}{25R^{2}}

Net force F_{1}+F_{2}=0

F_{1}=-F_{2}

If m is diplaced slightly by x from P to A

PA=(5R-x)\; and\; PB=(5R+x)

F_{1}=\frac{GMm}{(5R-x)^{2}}

F_{2}=\frac{GMm}{(5R+x)^{2}}

F_{2}<F_{1}

This results in an unstable equilibrium.

Posted by

infoexpert23

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