An atom \({ }_3^8 X\) is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleons is recorded by :

A nucleus has mass number \(\alpha\) and radius \(R_{\alpha}\). Another nucleus has mass number \(\beta\) and radius \(R_{\beta}\). If \(\beta = 8\alpha\) then \(R_{\alpha}/R_{\beta}\) is :

For a transistor to act as a switch, it must be operated in

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is ___________ m.
\(\left( g =10 m / s ^2\right)\)

A square shaped coil of area \(70\,cm ^2\) having \(600\) turns rotates in a magnetic field of \(0.4\,wbm ^{-2}\), about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes \(500\) revolution in a minute, the instantaneous emf when the plane of the coil is inclined at \(60^{\circ}\) with the field, will be \(..........V\). (Take \(\pi=\frac{22}{7}\) )

Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is _______.

If the charge on a capacitor is increased by \(2C\), the energy stored in it increases by \(44 \%\). The original charge on the capacitor is (in \(C\) )

Eight equal drops of water are falling through air with a steady speed of \(10\,cm / s\). If the drops coalesce, the new velocity is \(.........\,cm/s\)

Two isolated conducting spheres \(S_{1}\) and \(S_{2}\) of radius \(\frac{2}{3} R\) and \(\frac{1}{3} R\) have \(12\, \mu C\) and \(-3\, \mu C\) charges, respectively, and are at a large distance from each other. They are now  onnected by a conducting wire. A long time after this is done the charges on \(S_{1}\) and \(S_{2}\) are respectively

The total length of a sonometer wire between fixed ends is \(110\, cm\). Two bridges are placed to divide the length of wire in ratio \(6 : 3 : 2\). The tension in the wire is \(400\, N\) and the mass per unit length is \(0.01\, kg/m\) . What is the minimum common frequency with Which three parts can vibrate ........... \(Hz\) ?

A simple pendulum of length \(L\) is placed between the plates of a parallel plate capacitor having electric field \(E,\) as shown in figure. Its bob has mass \(m\) and charge \(q.\) the time period of the pendulum is given by

In the following circuit, the switch \(S\)  is closed at \(t = 0.\)  The charge on the capacitor  \(C_1\)  as a function of time will be given by \(\left( {{C_{eq}}\, = {\kern 1pt} \,\frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}} \right).\)