Capacitance (C) is defined as the ratio of charge (q) to potential difference (V):
$C = \frac{q}{V}$
However, capacitance is primarily determined by the geometry of the capacitor (plate area, separation between plates, dielectric material). The charge (q) and potential difference (V) are related to the capacitance but do not determine it. A capacitor with a specific geometry will have a fixed capacitance.
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is :
The current passing through the battery in the given circuit, is:
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :