A tuning fork having frequency of 340 Hz is vibrated just above a cylindrical tube. The height of the tube is 120 cm. Water is slowly poured in. The minimum height of water for ( v = 340 m/s) resonance is

1) 25 cm
2) 45 cm
3) 75 cm
4) 95 cm 

The moment of inertia of a sphere of mass M and radius R about an axis passing through its centre 
is 2 / 5MR². The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is

1) 7/5R      2) 3/5R    3)     4) 

When $$5\,V$$ potential difference is applied across a wire of length $$0.1\,m$$, the drift speed of electrons is $$25\times10^{-4}$$ $$ms^{-1}$$. If the electron density in the wire is $$8\times10^{28} m^{-3}$$ the resistivity of the material is close to

1) $$1.6\times10^{-8}\Omega\,m$$
2) $$1.6\times10^{-7}\Omega\,m$$
3) $$1.6\times10^{-5}\Omega\,m$$
4) $$1.6\times10^{-6}\Omega\,m$$

A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading 58.5 degree.
Vernier scale reading 9 division.
Given that, I division on main scale corresponds to 0.5 degree. Total division on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data is

1) 58.59°
2) 59.77°
3) 58.65°
4) 59°

A large number of liquid drops each of radius r coalesce to from a single drop of radius R. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is
[Given surface tension of liquid T, density $$\rho$$]

1) $$\sqrt{\frac{T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)} $$
2) $$\sqrt{\frac{2T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)} $$
3) $$\sqrt{\frac{4T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)} $$
4) $$\sqrt{\frac{6T}{\rho}\left(\frac{1}{r}-\frac{1}{R}\right)} $$

Parallel plate air capacitor has capacitance C when it is half filled with a dielectric constant ∑ _r = 5; the percentage increase in capacitance will be

1) 400%
2) 66.6%
3) 33.3%
4) 200%

Parallel rays of light of intensity I=912 Wm^-2 are incident on a spherical block body kept in surroundings of temperature 300 K Take Stefan constant σ=5.7×10-8 Wm^-2 K^-4 and assume that energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to

1) 330 K
2) 660 K
3) 960 K
4) 1550 K

The sample of the same gas, x, y and z, for which the ratio of specific heats γ =3/2 have initially the same volume. The volume of the each sample is doubled by adiabatic process in the case of x, by isobaric process in the case of y and by isothermal process in the case of z. If the initial pressure of the sample of x, y and z are in the ratio 2Ö 2 : 1 : 2 then the ratio of the their final pressures is  

1) 2 : 1 : 1
2) 1 : 1 : 1
3) 1 : 2 : 1
4) 1 : 1 : 2 

A lead bullet strikes against a steel plate with a velocity 200 m/s. If the impact is perfectly inelastic and the heat produced is equally shared between the bullet and the target, then the rise in temperature of the bullet is (specific heat capacity of lead =125 Jkg ^-1 K ^-1)

1) 80° C
2) 60° C
3) 40° C
4) 120° C

The charge on the capacitor of capacitance C shown in the figure below will be