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

A galvanometer having a resistance of \(20\,\Omega \) and \(30\, divisions\) on both sides has figure of merit \(0.005\, ampere /division\). The resistance that should be connected in series such that it can be used as a voltmeter upto \(15\, volt\) is ........... \(\Omega\)

A person lives in a high-rise building on the bank of a river \(50\, m\) wide. Across the river is a well lit tower of height \(40\, m\). When the person, who is at a height of \(10\, m\), looks through a polarizer at an appropriate angle at light of the tower reflecting from the river surface, he notes that intensity of light coming from distance \(X\) from his building is the least and this corresponds to the light coming from light bulbs at height \('Y'\) on the tower. The values of \(X\) and \(Y\) are respectively close to (refractive index of water \(  \simeq  \frac{4}{3})\)

A satellite of mass \(M\) is in a circular orbit of radius \(R\) about the centre of the earth. A meteorite of the same mass, falling towards the earth collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be

Boolean relation at the output stage\(-Y\) for the following circuit is

A river is flowing from west to east direction with speed of \(9 \mathrm{~km} \mathrm{~h}^{-1}\). If a boat capable of moving at a maximum speed of \(27 \mathrm{~km} \mathrm{~h}^{-1}\) in still water, crosses the river in half a minute, while moving with maximum speed at an angle of \(150^{\circ}\) to direction of river flow, then the width of the river is :

A torque meter is calibrated to reference standards of mass, length and time each with \(5 \%\) accuracy. After calibration, the measured torque with this torque meter will have net accuracy of\(............\%\)

The force of interaction between two atoms is given by \(F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);\) where \(x\) is the distance, \(k\) is the Boltzmann constant and \(T\) is temperature and \(\alpha \) and \(\beta \) are two constants. The dimension of \(\beta \) is

A diatomic gas \((\gamma=1.4)\) does \(100 \mathrm{~J}\) of work in an isobaric expansion. The heat given to the gas is _______.

When 300 J of heat given to an ideal gas with \(C _{ p }=\frac{7}{2} R\) its temperature raises from \(20{ }^{\circ} C\) to \(50^{\circ} C\) keeping its volume constant. The mass of the gas is (approximately) _________ g. \(( R =8.314 J / mol . K )\).

A zener diode of power rating \(1.6\,W\) is to be used as voltage regulator. If the zener diode has a breakdown of \(8\,V\) and it has to regulate voltage fluctuating between \(3\,V\) and \(10 \,V\). The value of resistance \(R_5\) for safe operation of diode will be \(.........\Omega\)

A block takes \(t\) time to slide down a plane inclined at \(45°\) to the horizontal. If the surface is made smooth (frictionless), the block takes time \(\dfrac{t}{2}\) to slide down the plane. The coefficient of friction between the block and the inclined plane is \(\left(\dfrac{\alpha}{100}\right)\). The value of \(\alpha\) is __________.

For a plane electromagnetic wave, the magnetic field at a point \(x\) and time \(t\) is \(\overrightarrow{ B }( x , t )=\left[1.2 \times 10^{-7} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ k }\right] T\) The instantaneous electric field \(\overrightarrow{ E }\) corresponding to \(\overrightarrow{ B }\) is : (speed of light \(\left.c=3 \times 10^{8} ms ^{-1}\right)\)