Two stars are \(10\) light years away from the earth. They are seen through a telescope of objective diameter \(30\, cm\). The wavelength of light is \(600\, nm\). To see the stars just resolved by the telescope, the minimum distance between them should be ( \(1\) light year \(= 9.46 \times 10^{15}\, m\)) of the order of

A submarine experiences a pressure of \(5.05\times 10^6\,Pa\) at a depth of \(d_1\) in a sea. When it goes further to a depth of \(d_2,\) it experiences a pressure of \(8.08\times 10^6\,Pa.\) Then \(d_2 -d_1\) is approximately ........ \(m\) (density of water \(= 10^3\,kg/m^3\) and acceleration due to gravity \(= 10\,ms^{-2}\) )

In Young's double slits experiment, the position of \(5^{\text {th }}\) bright fringe from the central maximum is \(5\,cm\). The distance between slits and screen is \(1\,m\) and wavelength of used monochromatic light is \(600\,nm\). The separation between the slits is \(........\mu m\)

If the charge on a capacitor is increased by \(2C\), the energy stored in it increases by \(44 \%\). The original charge on the capacitor is (in \(C\) )

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:

A uniform metal chain of mass \(m\) and length ' \(L\) ' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' \(l\) ' is hanging on one side and rest of its length ' \(L -l\) ' is hanging on the other side of the pulley. At a certain point of time, when \(l=\frac{L}{x}\), the acceleration of the chain is \(\frac{g}{2}\). The value of \(x\) is ........

A series \(LR\) circuit connected with an ac source \(E=(25 \sin 1000 t)\  V\) has a power factor of \(\frac{1}{\sqrt{2}}\). If the source of emf is changed to \(E=(20 \sin 2000 t)\ V,\) the new power factor of the circuit will be _______.

In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is ___________ mm.
[Assume least count is 0.01 mm ]

The equivalent resistance between \(A\) and \(B\) of the network shown in figure

A given object takes \(n\) times the time to slide down \(45^{\circ}\) rough inclined plane as it takes the time to slide down an identical perfectly smooth \(45^{\circ}\) inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is _______.

A convex lens is made from glass material having refractive index of \(1.4\) with same radius of curvature on both sides. The ratio of its focal length and radius of curvature is ______.