A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of $$2:1.$$ The ratio of their nuclear sizes will be

An $$\alpha$$-particle of energy $$5$$ $$MeV$$ is scattered through $$180^{\circ }$$ by a fixed uranium nucleus. The distance of closest approach is of the order of

If the temperature of the sun were to increase from $$T$$ to $$2T$$ and its radius from $$R$$ to $$2R$$, then the ratio of the radiant energy received on earth to what it was previously will be

One mole of ideal monatomic gas $$\left(\gamma =5/3\right)$$ is mixed with one mole of diatomic gas $$\left(\gamma =7/5\right)$$. What is $$\gamma$$ for the mixture? $$\gamma$$ Denotes the ratio of specific heat at constant pressure, to that at constant volume

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $$K$$ and $$2K$$ and thickness $$x$$ and $$4x,$$ respectively, are $$T_2$$ and $$T_1\left(T_2>T_1\right).$$ The rate of heat transfer through the slab, in a steady state is \left( {{{A\left( {{T_2} - {T_1}} \right)K} \over x}} \right)f, with $$f$$ equal to

Time taken by a $$836$$ $$W$$ heater to heat one litre of water from $$10{}^{\circ }C$$ to $$40{}^{\circ }C$$ is

Two thermally insulated vessels $$1$$ and $$2$$ are filled with air at temperatures $$\left(T_1,T_2\right),$$ volume $$\left(V_1,V_2\right)$$ and pressure $$\left(P_1,P_2\right)$$ respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

Which of the following statements is correct for any thermodynamic system ?

Two spherical conductors $$B$$ and $$C$$ having equal radii and carrying equal charges on them repel each other with a force $$F$$ when kept apart at some distance. A third spherical conductor having same radius as that $$B$$ but uncharged is brought in contact with $$B,$$ then brought in correct with $$C$$ and finally removed away from both. The new force of repulsion between $$B$$ and $$C$$ is

A charge particle $${}^{\prime }{q}^{\prime }$$ is shot towards another charged particle $${}^{\prime }{Q}^{\prime }$$ which is fixed, with a speed $${}^{\prime }{v}^{\prime }$$. It approaches $${}^{\prime }{Q}^{\prime }$$ upto a closest distance $$r$$ and then returns. If $$q$$ were given a speed of $${}^{\prime }2v^{\prime }$$ the closest distances of approaches would be

Four charges equal to -$$Q$$ are placed at the four corners of a square and a charge $$q$$ is at its center. If the system is in equilibrium the value of $$q$$ is

A charged oil drop is suspended in a uniform field of $$3\times 10^4$$ $$v/m$$ so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge $$=9.9\times 10^{-15}kg$$ and $$g=10m/s^2$$)

A projectile can have the same range 'R' for two angles of projection. If T1 and T2 be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

A ball is thrown from a point with a speed ν0 at an angle of projection θ. From the same point and at the same instant person starts running with a constant speed {{{v_0}} \over 2} to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection θ?

An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e 120 km/h, the stopping distance will be

A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in {T \over 3} seconds?

The work function of a substance is $$4.0$$ $$eV.$$ The longest wavelength of light that can cause photo-electron emission from this substance is approximately.

According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal $$Vs$$ the frequency, of the incident radiation gives as straight the whose slope

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is $$2s.$$ The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be

The materials suitable for making electromagnets should have