A tuning fork of known frequency $$256$$ $$Hz$$ makes $$5$$ beats per second with the vibrating string of a piano. The beat frequency decreases to $$2$$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor

Dimensions of $${1 \over {{\mu _0}{\varepsilon _0}}}$$, where symbols have their usual meaning, are

The physical quantities not having same dimensions are