JEE (Advanced) 2011 Paper-2

Which of the following statement(s) is/are correct?

A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision

A train is moving along a straight line with a constant acceleration ‘a’. A boy standing in the train throwsa ball forward with a speed of 10 m/s, at an angle of $$60^\circ$$ to the horizontal. The boy has to move forward by 1.15 m inside the train to catch the ball backat the initial height. The acceleration of the train, in $$m/s^2$$, is

A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is

Two batteries of different emfs and different internal resistances are connected as shown. The voltage across AB in volts is

Water (with refractive index = $$\frac{4}{3}$$) in a tank is 18 cm deep. Oil of refractive index $$\frac{7}{4}$$ lies on water making a convex surface of radius of curvature ‘R = 6 cm’ as shown. Consider oil to act as a thin lens. An object ‘S’ is placed 24 cm above water surface. The location of its image is at ‘x’ cm above the bottom of the tank. Then ‘x’ is

A series R-C combination is connected to an AC voltage of angular frequency $$\omega = 500$$ radian/s. If the impedance of the R-C circuit is $$R\sqrt{1.25}$$, the time constant
(in millisecond) of the circuit is

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is $$A \times 10^Z$$ (where 1 < A < 10). The value of ‘Z’ is

One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I.

Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as $$\lambda_f$$. Match each system with statements given in Column II describing the nature and wavelength of the standing waves.