In a Young's double slit experiment, the slits are separated by 0.2 mm. If the slits separation is increased to 0.4 mm , the percentage change of the fringe width is _______.

A body of mass ' \(m\) ' connected to a massless and unstretchable string goes in verticle circle of radius ' \(R\) 'under gravity \(g\). The other end of the string is fixed at the center of circle. If velocity at top of circular path is \(n \sqrt{g R}\), where, \(n \geqslant 1\), then ratio of kinetic energy of the body at bottom to that at top of the circle is

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

List \(I\) (Physical Quantity)	List \(II\) (Dimensional Formula)
\((A)\) Pressure gradient	\((I)\) \(\left[ M ^0 L ^2 T ^{-2}\right]\)
\((B)\) Energy density	\((II)\) \(\left[ M ^1 L ^{-1} T ^{-2}\right]\)
\((C)\) Electric Field	\((III)\) \(\left[ M ^1 L ^{-2} T ^{-2}\right]\)
\((D)\) Latent heat	\((IV)\) \(\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]\)

Choose the correct answer from the options given below:

An \(AC\) source rated \(220\, V , 50\, Hz\) is connected to a resistor. The time taken by the current to change from its maximum to the rms value is

An inductor of inductance \(10\) mH having resistance of \(100\,\Omega\) is connected to battery of E.M.F. \(1.0\) V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is \(2\) mA and \(4\) mA is _______.

Find out the surface charge density at the intersection of point \(x =3\, m\) plane and \(x\) -axis, in the region of uniform line charge of \(8\, nC / m\) lying along the \(z\) -axis in free space.

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ' \(h\) ' in terms of the angle of incidence ' \(i\) ' and angle of refraction ' \(r\) ', if the glass slab is placed in air medium?

Abeam of unpolarised light of intensity \(I_0\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of \(45^{\circ}\) relative to that of \(A\). The intensity of emergent light is :

The displacement x versus time graph is shown below.

(A) The average velocity during 0 to 3 s is \(10 \mathrm{~m} / \mathrm{s}\)
(B) The average velocity during 3 to 5 s is \(0 \mathrm{~m} / \mathrm{s}\)
(C) The instantaneous velocity at \(\mathrm{t}=2 \mathrm{~s}\) is \(5 \mathrm{~m} / \mathrm{s}\)
(D) The average velocity during 5 to 7 s and instantaneous velocity at \(\mathrm{t}=6.5 \mathrm{~s}\) are equal
(E) The average velocity from \(t=0\) to \(t=9 \mathrm{~s}\) is zero
Choose the correct answer from the options given below:

Eight mercury drops, each of radius \(r\), coalesce to form a bigger drop. The surface energy released in this process is _______. (\(S\) is the surface tension of mercury).

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should by unbinding the strings to achieve a speed of \(4\,ms ^{-1}\), is\(........cm\). \(\left(\right.\) take \(\left.g=10\,ms ^{-2}\right)\)

The equilateral triangle \(ABC\) is cut from a thin solid sheet of wood. (See figure) \(D, E\) and \(F\) are the mid points of its sides as shown and \(G\) is the centre of the triangle. The moment of inertia of the triangle about an axis passing through \(G\) and perpendicular to the plane of the triangle is \(I_0.\) If the smaller triangle \(DEF\) is removed from \(ABC,\) the moment of inertia of the remaining figure about the same axis is \(I.\) Then

A uniform electric field of \(10\,N / C\) is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy \(0.5\,eV\). The length of each plate is \(10\,cm\). The angle \((\theta)\) of deviation of the path of electron as it comes out of the field is  \(.........\)(in degree).