JEE (Advanced) 2009 Paper-2

Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions $$\phi_p = 2.0$$ eV, $$\phi_q = 2.5$$ eV and $$\phi_r = 3.0$$ eV, respectively. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensities illuminates each of the plates. The correct I-V graph for the experiment is [Take hc = 1240 eV nm]

A uniform rod of length L and mass M is pivoted at the centre. Its two ends are attached to two springs of equal spring constants k. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $$\theta$$ in one direction and released. The frequency of oscillation is

Two metallic rings A and B, identical in shape and size but having different resistivities $$\rho_A$$ and $$\rho_B$$, are kept on top of two identical solenoids as shown in the figure. When current J is switched on in both the solenoids in identical manner, the rings A and B jump to heights $$h_A$$ and $$h_B$$, respectively, with $$h_A > h_B$$. The possible relation(s) between their resistivities and their masses $$m_A$$ and $$m_B$$ is(are)

A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonanceandthat with the longer air-column is the second resonance. Then,

The figure shows the P-V plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semi-circle and CDA is half of an ellipse. Then, 

Under the influence of the Coulomb field of charge +Q, a charge -q is moving around it in an elliptical orbit. Find out the correct statement(s).

A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then,

Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process(es) from Column II.

Column I shows four situations of standard Young’s double slit arrangement with the screen placed far away from the slits $$S_1$$ and $$S_2$$. In each of these cases $$S_1P_0 = S_2P_0, S_1P_1 - S_2P_1 = \frac{\lambda}{4}$$ and $$S_1P_2 - S_2P_2 = \frac{\lambda}{3}$$, where $$\lambda$$ is the wavelength of the light used. In the cases B, C and D, a transparent sheet of refractive index $$\mu$$ and thickness t is pasted on slit $$S_2$$. The thicknesses of the sheets are different in different cases. The phase difference between thelight waves reaching a point P on the screen from the two slits is denoted by $$\delta(P)$$ and the intensity by $$I(P)$$. Match each situation given in Column I with the statement(s) in Column II valid for that situation.

A metal rod AB of length 10x has its one end A in ice at $$0^\circ C$$ and the other end B in water at $$100^\circ C$$. If a point P on the rod is maintained at $$400^\circ C$$, then it is found that equal amounts of water andice evaporate and melt per unit time. The latent heat of evaporation of water is 540 cal/g and latent heat of melting of ice is 80 cal/g. If the point P is at a distance of $$\lambda x$$ from the ice end A, find the value of $$\lambda$$. [Neglect any heat loss to the surrounding.]