An electric dipole of dipole moment \(6 \times 10^{-6} \mathrm{Cm}\) is placed in uniform electric field of magnitude \(10^6 \mathrm{~V} / \mathrm{m}\). Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J.

In a Young’s double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is \(1/8^{th}\) of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio \(2:2:3\). The two pieces of equal masses fly off perpendicular to each other with a speed of \(18~m/s\) each. The velocity of the heavier fragment is ___________ \(m/s\).

A sample of an ideal gas is taken through the cyclic process \(abca\) as shown in the figure. The change in the internal energy of the gas along the path \(ca\) is \(-180\, J\). The gas absorbs \(250\, J\) of heat along the path \(ab\) and \(60\, J\) along the path \(bc\). The work done by the gas along the path \(abc\) is ..... \(J\)

For the given circuit, in the steady state, \(\left| V _{ B }- V _{ D }\right|=.......V.\)

In a compound microscope, the magnified virtual image is formed at a distance of \(25\, cm\) from the eye-piece. The focal length of its objective lens is \(1\, cm .\) If the magnification is \(100\) and the tube length of the microscope is \(20\, cm ,\) then the focal length of the eye-piece lens (in \(cm\) ) is

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are \(100\) divisions in circular scale and pitch of screw gauge is \(0.1\) mm. When diameter of a sphere is measured, the reading of main scale is \(5\) mm and \(50^{\text{th}}\) division of circular scale coincides with the reference line of main scale. The diameter of sphere is _______ mm.

A block of mass \(1 \,kg\) attached to a spring is made to oscillate with an initial amplitude of \(12\, cm\). After \(2\, minutes\) the amplitude decreases to \(6\, cm\). Determine the value of the damping constant for this motion. (take In \(2=0.693\) )

A particle moving in a circle of radius \(R\) with uniform speed takes time \(\mathrm{T}\) to complete one revolution. If this particle is projected with the same speed at an angle \(\theta\) to the horizontal, the maximum height attained by it is equal to \(4 R\). The angle of projection \(\theta\) is then given by _______.

A parallel plate capacitor has plate of length \('l',\) width \('w'\) and separation of plates is \('d'.\) It is connected to a battery of emf \(V\). A dielectric slab of the same thickness '\(d\)' and of dielectric constant \(k =4\) is being inserted between the plates of the capacitor. At what length of the slab inside plates, will be energy stored in the capacitor be two times the initial energy stored\(?\)

A new unit \((\alpha)\) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of \(\alpha\) units if light takes \(6\) min. \(40\) s to cover this distance?

In a reflecting telescope, a secondary mirror is used to: