A galvanometer coil has \(500\) turns and each turn has an average area of \(3 \times 10^{-4}\, m ^{2}\). If a torque of \(1.5\,Nm\) is required to keep this coil parallel to magnetic field when a current of \(0.5\, A\) is flowing through it, the strength of the field (in \(T )\) is

A convex lens of focal length \(40 \mathrm{~cm}\) forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length \(20 \mathrm{~cm}\). The photoelectric current now is:

Match List \(I\) with List \(II\)

List - \(I\)	List - \(II\)
\((A)\) Torque	\((I)\) \({\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}\)
\((B)\) Magnetic fileld	\((II)\) \(\left[\mathrm{L}^2 \mathrm{~A}^1\right]\)
\((C)\) Magneti moment	\((III)\) \({\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}\)
\((D)\) permeability of free space	\((IV)\) \(\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)

Choose the correct answer from the options given below :

An electric bulb rated \(50 \mathrm{~W}-200 \mathrm{~V}\) is connected across a \(100 \mathrm{~V}\) supply. The power dissipation of the bulb is _______.

A coil of cross-sectional area  \(A\) having \(n\)  turns is placed in a uniform magnetic field \(B.\)  When it is rotated with an angular velocity \(\omega ,\)  the maximum \(e.m.f.\)  induced in the coil will be

The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is \(\frac{\pi}{2}\) at point \(P\) and \(\pi\) at point \(Q\). Then the difference between the resultant intensities at \(P\) and \(Q\) will be.......\(I\)

Two satellites \(A\) and \(B\) having masses in the ratio \(4: 3\) are revolving in circular orbits of radii \(3\,r\) and \(4\,r\) respectively around the earth. The ratio of total mechanical energy of \(A\) to \(B\) is.

A rod of length \(L\) has non-uniform linear mass density given by \(\rho(\mathrm{x})=\mathrm{a}+\mathrm{b}\left(\frac{\mathrm{x}}{\mathrm{L}}\right)^{2},\) where \(a\) and \(\mathrm{b}\) are constants and \(0 \leq \mathrm{x} \leq \mathrm{L}\). The value of \(\mathrm{x}\) for the centre of mass of the rod is at

Consider a moving coil galvanomenter (MCG):
A. The torsional constant in moving coil galvanometer has dimentions \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\)
B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C. If we increase number of turns \((\mathrm{N})\) to its double \((2 \mathrm{~N})\), then the voltage sensitivity doubles.
D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.
E. Current sensitivity of MCG depends inversely on number of turns of coil.
Choose the correct answer from the options given below:

Eight copper wire of length \(l\) and diameter \(d\) are joined in parallel to form a single composite conductor of resistance \(R\). If a single copper wire of length \(2\,l\) have the same resistance \((R)\) then its diameter will be \(.....d\).

A uniformly thick wheel with moment of inertia \(I\) and radius \(R\) is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses \(\mathrm{m}_{1}\) and \(\mathrm{m}_{2}\left(\mathrm{m}_{1}>\mathrm{m}_{2}\right)\) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when \(\mathrm{m}_{1}\) descents by a distance \(h\) is

In a series \(LCR\) circuit, the inductance, capacitance and resistance are \(L =100\, mH , C =100 \mu F\) and \(R =\) \(10 \Omega\) respectively. They are connected to an \(AC\) source of voltage \(220\, V\) and frequency of \(50\, Hz\). The approximate value of current in the circuit will be.....\(A.\)

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be \(....m\) Given, the length of the rod is \(10 \sqrt{3} m\).