A double slit interference experiment performed with a light of wavelength 600 nm forms an interference fringe pattern on a screen with 10 th bright fringe having its centre at a distance of 10 mm from the central maximum. Distance of the centre of the same 10th bright fringe from the central maximum when the source of light is replaced by another source of wavelength 660 nm would be _________ mm .

A resistor dissipates \(192\, {J}\) of energy in \(1\, {s}\) when a current of \(4\, {A}\) is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in \(5 \,{s}\) in \(.....\,J.\)

Two small spherical balls of mass 10 g each with charges \(-2 \mu \mathrm{C}\) and \(2 \mu \mathrm{C}\), are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of \(100 \mu \mathrm{C} / \mathrm{m}^2\) such that length of rod makes an angle of \(30^{\circ}\) with electric field generated by charge sheet. Net torque acting on the rod is:
(Take \(\varepsilon_0: 8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\))

In the given figure, the face \(AC\) of the equilateral prism is immersed in a liquid of refractive index ' \(n\) '. For incident angle \(60^{\circ}\) at the side \(AC\), the refracted light beam just grazes along face \(AC\). The refractive index of the liquid \(n =\frac{\sqrt{ x }}{4}\). The value of \(x...\) is (Given refractive index of glass \(=1.5\) )

In the given circuit all resistances are of value \(R\,ohm\) each. The equivalent resistance between \(A\) and \(B\) is 

A thin infinite sheet charge and an infinite line charge of respective charge densities \(+\sigma\) and \(+\lambda\) are placed parallel at \(5\,m\) distance from each other. Points \(P\) and \(Q\), are at \(\frac{3}{\pi} m\) and \(\frac{4}{\pi} m\) perpendicular distance from line charge towards sheet charge, respectively. \(E_P\) and \(E_Q\) are the magnitudes of resultant electric field intensities at point \(P\) and \(Q\), respectively. If \(\frac{E_p}{E_Q}=\frac{4}{a}\) for \(2|\sigma|=|\lambda|\). Then the value of \(a\) is ...........

particle moves with simple harmonic motion in a straight line. In first \(\tau\ s\), after starting from rest it travels a distance \(a\), and in next \(\tau\ s\) it travels \(2a\), in same direction, then

Two bodies are having kinetic energies in the ratio \(16: 9\). If they have same linear momentum, the ratio of their masses respectively is

The angular frequency of the damped oscillator is given by, \(\omega  = \sqrt {\left( {\frac{k}{m} - \frac{{{r^2}}}{{4{m^2}}}} \right)} \) where \(k\) is the spring constant, \(m\) is the mass of the oscillator and \(r\) is the damping constant. If the ratio \(\frac{{{r^2}}}{{mk}}\) is \(8\%\), the change in time period compared to the undamped oscillator is approximately as follows

When an object is kept at a distance of \(30\, cm\) from a concave mirror, the image is formed at a distance of \(10\, cm\) from the mirror. If the object is moved with a speed of \(9\, cms ^{-1}\), the speed (in \(cms ^{-1}\) ) with which image moves at that instant is\(....m/s\)