An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $$M.$$ The piston and the cylinder have equal cross sectional area $$A$$. When the piston is in equilibrium, the volume of the gas is $$V_0$$ and its pressure is $$P_0.$$ The piston is slightly displaced from the equilibrium position and released,. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frquency

The magnetic field in a travelling electromagnetic wave has a peak value of $$20$$ $$n$$$$T$$. The peak value of electric field strength is :

In an $$LCR$$ circuit as shown below both switches are open initially. Now switch $$S_1$$ is closed, $$S_2$$ kept open. ($$q$$ is charge on the capacitor and $$\tau$$ $$=RC$$ is Capacitance time constant). Which of the following statement is correct ?

In a hydrogen like atom electron make transition from an energy level with quantum number $$n$$ to another with quantum number $$\left(n-1\right)$$. If $$n>>1,$$ the frequency of radiation emitted is proportional to :

The above $$p$$-$$v$$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible ? The surface tension is $$T,$$ density of liquid is $$\rho$$ and $$L$$ is its latent heat of vaporization.

Two charges, each equals to $$q,$$ are kept at $$x=-a$$ and $$x=a$$ on the $$x$$-axis. A particle of mass $$m$$ and charge {q_0} = {q \over 2} is placed at the origin. If charge $$q_0$$ is given a small displacement $$\left(y<<a\right)$$ along the $$y$$-axis, the net force acting on the particle is proportional to

A charge $$Q$$ is uniformly distributed over a long rod $$AB$$ of length $$L$$ as shown in the figure. The electric potential at the point $$O$$ lying at distance $$L$$ from the end $$A$$ is

A projectile is given an initial velocity of $$\left(\hat{i}+2\hat{j}\right)$$ m/s, where $$\hat{i}$$ is along the ground and $$\hat{j}$$ is along the vertical. If g = 10 m/s2, the equation of its trajectory is:

The anode voltage of a photocell is kept fixed. The wavelength $$\lambda$$ of the light falling on the cathode is gradually changed. The plate current $$I$$ of the photocell varies as follows :

Two short bar magnets of length $$1$$ $$cm$$ each have magnetic moments $$1.20$$ $$A{m}^2$$ and $$1.00$$ $$A{m}^2$$ respectively. They are placed on a horizontal table parallel to each other with their $$N$$ poles pointing towards the South. They have a common magnetic equator and are separated by a distance of $$20.0$$ $$cm.$$ The value of the resultant horizontal magnetic induction at the mid-point $$O$$ of the line joining their centres is close to $$($$ Horizontal component of earth's magnetic induction is $$3.6\times 10.5Wb/m^2)$$

What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and radius $$R$$ in a circular orbit at an altitude of $$2R$$?

Two coherent point sources $$S_1$$ and $$S_2$$ are separated by a small distance $${}^{\prime }{d}^{\prime }$$ as shown. The fringes obtained on the screen will be

A beam of unpolarised light of intensity $${\mathrm{I}}_0$$ is passed through a polaroid $$A$$ and then through another polaroid $$B$$ which is oriented so that its principal plane makes an angle of $$45^{\circ }$$ relative to that of $$A$$. The intensity of the emergent light is

Two capacitors $$C_1$$ and $$C_2$$ are charged to $$120$$ $$V$$ and $$200$$ $$V$$ respectively. It is found that connecting them together the potential on each one can be made zero. Then

A sonometer wire of length $$1.5$$ $$m$$ is made of steel. The tension in it produces an elastic strain of $$1\%$$. What is the fundamental frequency of steel if density and elasticity of steel are $$7.7\times 10^{3}kg/m^3$$ and $$2.2\times 10^{11}N/m^2$$ respectively ?

A circular loop of radius $$0.3$$ $$cm$$ lies center of the small loop is on the axis of the bigger loop. The distance between their centers is $$15$$ $$cm.$$ If a current of $$2.0$$ $$A$$ flows through the smaller loop, than the flux linked with bigger loop is

A metallic rod of length $${}^{\prime }{\ell }^{\prime }$$ is tied to a string of length $$2$$$$\ell$$ and made to rotate with angular speed $$w$$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $${}^{\prime }{B}^{\prime }$$ in the region, the $$e.m.f$$ induced across the ends of the rod is

A hoop of radius $$r$$ and mass $$m$$ rotating with an angular velocity $${\omega }_0$$ is placed on a rough horizontal surface. The initial velocity of the center of the hoop is zero. What will be the velocity of the center of the hoop when it cases to slip?

For gaseous state, if most probable speed is denoted by C*, average speed by $$\stackrel{\_\_}{C}$$ and mean square speed by C, then for a large number of molecules the ratios of these speeds are: