Two spheres having the same radius and mass are suspended by two strings of equal length from the same point, so that their surfaces touch each other. On depositing a charge of 4×10⁻⁶ C on them, they repel each other so that in equilibrium the angle between their strings becomes 60°. The distance f…

Question

Two spheres having the same radius and mass are suspended by two strings of equal length from the same point, so that their surfaces touch each other. On depositing a charge of 4×10⁻⁶ C on them, they repel each other so that in equilibrium the angle between their strings becomes 60°. The distance from the point of suspension to the centre of each sphere is 10 cm. Find the mass of each sphere. (K=9×10⁹ SI units, g=10 m s⁻²)

Accepted Answer

(2) 0.6235 kg. Given: total charge 4×10⁻⁶ C; angle between the strings 60°, so each string makes 30° with the vertical; L=10 cm=0.1 m from the support to each centre. The spheres are identical and touching when charged, so they share the charge equally: q=2×10⁻⁶ C each. Separation of the centres: d=2L sin 30°=2×0.1×0.5=0.1 m Repulsion: F=(Kq²)/(d²)=(9×10⁹×(2×10⁻⁶)²)/((0.1)²)=3.6 N Each sphere is held by the tension T, its weight mg and the repulsion F: T cos 30°=mg and T sin 30°=F, so tan 30°=F/(mg). m=F/(g tan 30°)=(3.6)/(10×0.5774)=0.6235 kg

Step-by-step solution

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