All Problems

Mechanical Oscillations

Problem 4.63

A small ball of mass \(m=21\) g suspended by an insulating thread at a height \(h=12 \mathrm{~cm}\) from a large horizontal conducting plane performs small oscillations (Fig. 4.22). After a charge \(q\) had been imparted to the ball, the oscillation period changed \(\eta=2.0\) times. Find \(\boldsymbol{q}\)

Reveal Answer
q=4hπε0mg(η21)=2.0μCq=4 h \sqrt{\pi \varepsilon_{0} m g\left(\eta^{2}-1\right)}=2.0 \mu \mathrm{C}