A system consist of a cylinder surrounded by a cylindrical shell. A cylinder is a radius R and is made of material of thermal conductivity K, whereas a cylindrical shell has inner radius R and outer radius ZR and is made of material of thermal conductivity twice as that of cylinder. Assuming the system in steady state and negligible heat loss across the cylindrical surface, find the effective thermal conductivity of the system, if the two ends of the combined system are maintained at two different temperatures.

• 3 K

• $\frac{2}{3}$K

• $\frac{7}{4}$K

• $\frac{5\mathrm{K}}{4}$

A bat emitting an ultrasonic wave of frequency 4.5 x 10' Hz at speed of 6 m/s between two parallel walls. The two frequencies heared by the bat will be

• 4.67 x 10⁴ Hz, 4.34 x 10⁴ Hz

• 4.34 x 10⁴ Hz, 4.67 x 10⁴ Hz

• 4.5 x 10⁴ Hz, 5.4 x 10⁴ Hz

• 4.67 x 10³ Hz, 4.34 x 10⁴ Hz

Two different isotherms representing the relationship between pressure p and volume V at a given temperature of the same ideal gas are shown for masses m₁ and m₂ , then

• Nothing can be predicted

• m₁ < m₂

• m₁ = m₂

• m₁ > m₂

A small spherical drop fall from rest in viscous liquid. Due to friction, heat is produced. The correct relation between the rate of production of heat and the radius of the spherical drop at terminal velocity will be

• $\frac{\mathrm{dH}}{\mathrm{dt}} \propto \frac{1}{{\mathrm{r}}^5}$

• $\frac{\mathrm{dH}}{\mathrm{dt}} \propto {\mathrm{r}}^4$

• $\frac{\mathrm{dH}}{\mathrm{dt}} \propto \frac{1}{{\mathrm{r}}^4}$

• $\frac{\mathrm{dH}}{\mathrm{dt}} \propto {\mathrm{r}}^5$

The slope of isothermal and adiabatic curves are related as

• isothermal curve slope= adiabatic curve slope

• isothermal curve slope = γ × adiabatic curve slope

• adiabatic curve slope = γ× isothermal curve slope

• adiabatic curve slope =$\frac{1}{2}$× isothermal curve slope

The volume of an ideal gas is doubled in an isothermal process. Then, which of the following is true?

• Work done by the gas is positive

• Work done by the gas is negative

• Internal energy of the system decreases

• Internal energy of the system increases

A transformer having efficiency of 75 % is working on 220 V and 4.4 kW power supply. If the current in the secondary coil is 5 A. What will be the voltage across secondary coil and the current in primary coil?

• V_s = 220 V, i_p = 20A

• V_s = 660 V, i_p = 15 A

• V_s = 660 V, i_p = 20 A

• V_s = 220 V, i_p = 15 A

A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by

• 2πR² E

• π R²/E

• R / E

• Zero

29.

A beam of light travelling along X-axis is described by the electric field E_v = 600 $\frac{\mathrm{V}}{\mathrm{m}}$. sin$\mathrm{\omega } \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right)$, the maximum magnetic force on a charge q = 2e, moving along Y-axis with the speed of 3 × 10⁸ m/s is 

• 19.2 × 10^-17 N

• 1.92 × 10^-17

• 0.192

• None of these

In the given figure, potential difference between A and B is

• 0 V

• 5 V

• 10 V

• 15 V