The surface of a metal is illuminated altemately with photons of energies \(E _{1}=4\, eV\) and \(E _{2}=2.5\, eV\) respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is \(2 .\) The work function of the metal in \(( eV )\) is\(......ev\)

In the potentiometer, when the cell in the secondary circuit is shunted with 4 \(\Omega\) resistance, the balance is obtained at the length 120 cm of wire. Now when the same cell is shunted with 12 \(\Omega\) resistance, the balance is shifted to a length of 180 cm. The internal resistance of cell is ___________ \(\Omega\).

Two short electric dipoles \(A\) and \(B\) having dipole moment \(p_1\) and \(p_2\) respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point \(x\) is making an angle of \(60°\) with the line joining points \(O\) and \(x\). The ratio of the dipole moments \(p_2/p_1\) is _______.

Given below are two statements : Statement \(I\) : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement \(II\) : The refractive indices are different for different wavelengths in dispersive medium.
In the light of the above statements, choose the correct answer from the options given below :

A ball of mass \(100 \,g\) is dropped from a height \(h =\) \(10\, cm\) on a platform fixed at the top of vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance \(\frac{ h }{2}\). The spring constant is.......... \(Nm^{-1}\) . (Use \(g=10\, ms ^{-2}\) )

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is \(1 \mathrm{~mm}\) and circular scale reading is equal to \(42\) divisions. Pitch of screw gauge is \(1 \mathrm{~mm}\) and it has \(100\) divisions on circular scale. The diameter of the wire is \(\frac{x}{50} \mathrm{~mm}\). The value of \(x\) is _______.

Which of the following circuits represents a forward biased diode?


Choose the correct answer from the options given below :

The heat absorbed by a system in going through the given cyclic process is _______.

Two satellites of masses \(m\) and \(3\,m\) revolve around the earth in circular orbits of radii \(r\) and \(3 r\) respectively. The ratio of orbital speeds of the satellites respectively is :

A thin biconvex lens is prepared from the glass (\(\mu=1.5\)) both curved surfaces of which have equal radii of \(20\) cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ________ cm.

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are \(8 \Omega\) and \(10 \Omega\) respectively. After inserting in a hot bath of temperature \(400^{\circ} \mathrm{C}\), the resistance of platinum wire is _______.

An ice cube of dimensions \(60\,cm \times 50\,cm \times 20\,cm\) is placed in an insulation box of wall thickness \(1\,cm\). The box keeping the ice cube at \(0^{\circ}\,C\) of temperature is brought to a room of temperature \(40^{\circ}\,C\). The rate of melting of ice is approximately. (Latent heat of fusion of ice is \(3.4 \times 10^{5}\,J\,kg ^{-1}\) and thermal conducting of insulation wall is \(0.05\,Wm ^{-10} C ^{-1}\) )