A certain charge \(Q\) is divided into two parts \(q\) and \((Q-q) .\) How should the charges \(Q\) and \(q\) be divided so that \(q\) and \((Q-q)\) placed at a certain distance apart experience maximum electrostatic repulsion?

Two particles \(A\) and \(B\) of equal mass \(M\) are moving with the same speed \(v\) as shown in the figure . They collide completely inelastically and move as a single particle \(C\). The angle \(\theta \) that the path of \(C\) makes with the \(X-\) axis is given by 

\(512\) identical drops of mercury are charged to a potential of \(2\, V\) each. The drops are joined to form a single drop. The potential of this drop is ......... \(V.\)

A bullet of mass \(20\,g\) has an initial speed of \(1\,ms^{-1}\) just before it starts penetrating a mud wall of thickness \(20\,cm.\) If the wall offers a mean resistances of \(2.5 \times 10^{-2}\,N,\) the speed of the bullet after emerging from the other side of the wall is close to .............. \(\mathrm{ms}^{-1}\)

Two small equal point charges of magnitude \(q\) are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle \(\theta \) from the vertical. If the mass of each charge is \(m,\) then the electrostatic potential at the centre of line joining them will be \(\left( {\frac{1}{{4\pi { \in _0}}} = k} \right).\)

A solid disc of radius \(20 \,{cm}\) and mass \(10\, {kg}\) is rotating with an angular velocity of \(600\, {rpm}\), about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in \(10\, {s}\, ......\, \pi \times \,10^{-1}\, {Nm}\).

Resistance of a wire at \(0^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C}\) and \(t^{\circ} \mathrm{C}\) is found to be \(10 \Omega, 10.2 \Omega\) and \(10.95 \Omega\) respectively. The temperature \(t\) in Kelvin scale is _______.

\(AC\) voltage \(V(t)=20\,sin\omega \,t\) of frequency \(50\, {Hz}\) is applied to a parallel plate capacitor. The separation between the plates is \(2\, {mm}\) and the area is \(1 \,{m}^{2}\). The amplitude of the oscillating displacement current for the applied \(AC\) voltage is ...... \(\mu {A}\). [Take \(\left.\varepsilon_{0}=8.85 \times 10^{-12} \,{F} / {m}\right]\)

For the circuit shown below, the current through the Zener diode is......\(mA\)

Two capacitors, each having capacitance \(40\,\mu F\) are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant \(K\) such that the equivalence capacitance of the system became \(24\,\mu F\). The value of \(K\) will be.