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If two spheres of mass 100 tonne each, r...

If two spheres of mass 100 tonne each, revolve diametrically opposite to each other in a circle of radius 1 m, what should be their velocities? (Take `g = 6.67 xx 10^(-11) N m^(2) kg^(-2)`)

Text Solution

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The centripetal force required for the circular motion is provided by the gravitational force of attraction. We can write `(mv^(2))/(r) = (Gm^(2))/(4r^(2))`
`v = sqrt((Gm)/(4r))`
Substituting the values where m = 100 ton = `10^(5)` kg, r = 1 m and `G = 6.67 xx 10^(-11) N m^(2) kg^(-2)`
`v = sqrt((6.67 xx 10^(-11) xx 10^(5))/(4))= sqrt((6.67 xx 10^(-6))/(4))`
`= sqrt(1.67) xx 10^(-3) ms^(-1)`
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