31.

A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water 

• $\frac{\mathrm{V}}{2}$

• $\frac{\mathrm{V}}{3}$

• $\frac{\mathrm{V}}{4}$

• V

A parallel plate capacitor with air as the dielectric has capacitance C. A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be

• $\left(\mathrm{K} + 3\right)\frac{\mathrm{C}}{4}$

• $\left(\mathrm{K} + 2\right)\frac{\mathrm{C}}{4}$

• $\left(\mathrm{K} + 1\right)\frac{\mathrm{C}}{4}$

• $\frac{\mathrm{KC}}{4}$

A coil of n number of turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current of strength I is passed through the coil, the magnetic field at its centre is

• $\frac{{\mathrm{\mu }}_{\mathrm{o}} \mathrm{nI}}{\left(\mathrm{b} - \mathrm{a}\right)} {\log }_{\mathrm{e}} \frac{\mathrm{a}}{\mathrm{b}}$

• $\frac{{\mathrm{\mu }}_{\mathrm{o}} \mathrm{n} \mathrm{I}}{2 \left(\mathrm{b} - \mathrm{a}\right)}$

• $\frac{2 {\mathrm{\mu }}_{\mathrm{o}} \mathrm{nI}}{\mathrm{b}}$

• $\frac{{\mathrm{\mu }}_{\mathrm{o}} \mathrm{nI}}{2 \left(\mathrm{b} - \mathrm{a}\right)} {\log }_{\mathrm{e}} \frac{\mathrm{b}}{\mathrm{a}}$

A magnetic field exerts no force on

• a magnet

• an unmagnetised iron bar

• a moving charge

• stationary charge

In an L-C-R circuit inductance is changed from L to L/2.To keep the same resonance frequency, C should be changed to

• 2 C

• $\frac{\mathrm{C}}{2}$

• 4 C

• $\frac{\mathrm{C}}{4}$

Which one of the following graph represents the variation of maximum kinetic energy (Ek) of the emitted electrons with frequency v in photoelectric effect correctly?         

A vessel of height 2 d is half filled with a liquid of refractive index $\sqrt{2}$  and the other half with a liquid of refractive index n (the given liquids are immiscible). Then, the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will be

• $\frac{\mathrm{n}}{\mathrm{d} \left(\mathrm{n} + \sqrt{2}\right)}$

• $\frac{\mathrm{d} \left(\mathrm{n} + \sqrt{2}\right)}{\mathrm{n} \sqrt{2}}$

• $\frac{\sqrt{2} \mathrm{n}}{\mathrm{d} \left(\mathrm{n} + \sqrt{2}\right)}$

• $\frac{\mathrm{nd}}{\mathrm{d} + \sqrt{2\mathrm{n}}}$

The two lenses of an achromatic doublet should have

• equal powers

• equal dispersive powers

• equal ratio of their power and dispersive power

• sum of the product of their powers and dispersive power equal to zero

The tip of a needle does not give a sharp image on a screen. This is due to

• polarisation

• interference

• diffraction

• None of these

The truth table given below is for (A and B are the inputs, Y is the output)

• NOR

• AND

• XOR

• NAND