Three point particles of masses \(1.0\; \mathrm{kg} .1 .5 \;\mathrm{kg}\) and \(2.5\; kg\) are placed at three comers of a right angle triangle of sides \(4.0\; \mathrm{cm}, 3.0 \;\mathrm{cm}\) and \(5.0\; \mathrm{cm}\) as shown in the figure. The center of mass of the system is at a point

Unpolarized light of intensity \(I\) is incident on a system of two polarizers, \(A\) followed by \(B.\)  The intensity of emergent light is \(I/2.\)  If a third polarizer \(C\)  is placed between \(A\) and \(B,\)  the intensity of emergent light is reduced to \(I/3 .\)  The angle between the polarizers \(A\) and \(C\) is \(\theta \) . Then

A stream of a positively charged particles having \(\frac{ q }{ m }=2 \times 10^{11} \frac{ C }{ kg }\) and velocity \(\overrightarrow{ v }_0=3 \times 10^7 \hat{ i ~ m} / s\) is deflected by an electric field \(1.8 \hat{ j } kV / m\). The electric field exists in a region of \(10 cm\) along \(x\) direction. Due to the electric field, the deflection of the charge particles in the \(y\) direction is \(...........mm\)

A series \(L-R\) circuit is connected to a battery of emf \(V\). If the circuit is switched on at \(t =0\), then the time at which the energy stored in the inductor reaches \(\left(\frac{1}{n}\right)\) times of its maximum value, is 

In a common emitter configuration with suitable bias, it is given than \(R_L\) is the load resistance and \(R_{BE}\)  is small signal dynamic resistance (input side). Then, voltage gain, current gain and power gain are given, respectively, by: [ \(\beta \) is current gain, \(I_B\) , \(I_C\) , \(I_E\) are respectively base, collector and emitter currents]

The output of the given circuit diagram is _______.

The one division of main scale of vernier callipers reads \(1\,mm\) and \(10\) divisions of Vernier scale is equal to the \(9\) divisions on main scale. When the two jaws of the instrument touch each other the \(zero\) of the Vernier lies to the right of \(zero\) of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the \(zero\) of the Vernier scale lies in between \(4.1\,cm\) and \(4.2\,cm\) and \(6^{\text {th }}\) Vernier division coincides with a main scale division. The diameter of the bob will be \(.............10^{-2}\,cm\)

A moving coil of galvanometer when shunted with \(2\,\Omega\) resistance gives a full scale deflection for a current of \(500\) mA. When a resistance of \(470\,\Omega\) is connected in series it gives a full scale deflection for \(10\) V potential applied on it. The value of resistance of galvanometer coil is __________ \(\Omega\).

In the figure shown, after the switch \(‘S’\) is turned from position \(‘A’\) to position \(‘B’\), the energy dissipated in the circuit in terms of capacitance \(‘C’\) and total charge \(‘Q’\) is