The galvanometer deflection, when key \(K_1\) is closed but \(K_2\) is open, equals \(\theta_0\) (see figure). On closing \(K_2\) also and adjusting \(R_2\) to \(5\,\Omega \) , the deflection in galvanometer becomes \(\frac{{\theta _0}}{5}\). The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]: .................. \(\Omega\)

A homogeneous solid cylindrical roller of radius \(R\) and mass \(M\) is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is

A \(12\,V\) battery connected to a coil of resistance \(6 \,\Omega\) through a switch, drives a constant current in the circuit. The switch is opened in \(1\,ms\). The emf induced across the coil is \(20 \;V\). The inductance of the coil is  ........... \(mH\)

The position of the image formed by the combination of lenses is _______. \(\mathrm{f}_1=10 \mathrm{~cm} \quad \mathrm{f}_2=10 \quad \mathrm{f}_3=30 \mathrm{~cm}\)

Consider a uniform cubical box of side \(a\) on a rough floor that is to be moved by applying minimum possible force \(F\) at a point \(b\) above its centre of mass (see figure). If the coefficient of friction is \(\mu=0.4,\) the maximum possible value of \(100 \times \frac{b}{a}\) for a box not to topple before moving is

A ray of light passing through a prism \((\mu=\sqrt{3})\) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ..... . (in degrees)

Uniform magnetic fields of different strengths \(\left(B_1\right.\) and \(B_2\)), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q , at the interface at an instant, moves into the region 2 with velocity \(v\) and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface?

(Consider the velocity of the particle to be normal to the magnetic field and \(B_2 \gt B_1\))

The supply voltage to room is \(120\ V\). The resistance of the lead wires is \(6\,\Omega\) . A \(60\ W\) bulb is already switched on. What is the decrease of voltage across the bulb, when a \(240\ W\) heater is switched on in parallel to the bulb? ............. \(V\)

An aluminium wire is stretched to make its length, \(0.4 \,\%\) larger. Then percentage change in resistance is \(.....\,\%\)

A circular loop of radius \(20\text{ cm}\) and resistance \(2\ \Omega\) is placed in a time varying magnetic field \(\vec{B} = (2t^2 + 2t + 3)\text{ T}\). At \(t = 0\), for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at \(t = 3\text{ s}\) is \(\dfrac{\alpha}{50}\text{ A}\). The value of \(\alpha\) is _______.
(Take \(\pi = 22/7\))

A nucleus has mass number \(A_1\) and volume \(V_1\). Another nucleus has mass number \(A_2\) and volume \(V_2\). If relation between mass number is \(A_2=4 A_1\), then \(\frac{V_2}{V_1}=\)_______.

The figure shows a Young’s double slit experimental setup. It is observed that when a thin transparent sheet of thickness \(t\) and refractive index \(\mu \) is put in front of one of the slits, the central maximum gets shifted by a distance equal to \(n\) fringe widths. If the wavelength of light used is \(\lambda ,\,t\) will be