JEE (Advanced) 2017 Paper-2
For the following questions answer them individually
Two coherent monochromatic point sources $$S_{1}$$ and $$S_{2}$$ of wavelength $$\lambda=600$$ nm are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance $$d=1.8$$ mm. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $$\triangle\theta$$. Which of the following options is/are correct?
A source of constant voltage V is connected to a resistance R and two ideal inductors $$L_{1}$$ and $$L_{2}$$ through a switch as shown. There is no mutual inductance between the two inductors. The switch S is initially open. At = 0, the switch is closed and current begins to flow. Which of the following options is/are correct?
A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is $$\theta$$ Which of the following statements about its motion is/are correct?
A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque $$\tau$$ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct?
Consider a simple 𝑅𝐶 circuit as shown in Figure 1.
Process 1: In the circuit the switch 𝑆 is closed at t = 0 and the capacitor is fully charged to voltage $$V_0$$ (i.e., charging continues for time $$T \gg RC$$). In the process some dissipation $$(E_D)$$ occurs across the resistance 𝑅. The amount of energy finally stored in the fully charged capacitor is $$E_c$$.
Process 2: In a different process the voltage is first set to $$\frac{V_0}{3}$$ and maintained for a charging time $$T \gg RC$$. Then the voltage is raised to $$\frac{2 V_0}{3}$$ without discharging the capacitor and again maintained for a time $$T \gg RC$$. The process is repeated one more time by raising the voltage
to $$V_0$$ and the capacitor is charged to the same final voltage $$V_0$$ as in Process 1.
These two processes are depicted in Figure 2.
In Process 1, the energy stored in the capacitor $$E_{C}$$ and heat dissipated across resistance $$E_{D}$$ are related by:
One twirls a circular ring (of mass M and radius R) near the tip of one’s finger as shown in Figure 1. In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is r. The finger rotates with an angular velocity $$\omega_{0}$$. The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact (Figure 2). The coefficient of friction between the ring and the finger is $$\mu$$ and the acceleration due to gravity is g
For the following questions answer them individually
Pure water freezes at 273 K and 1 bar. The addition of 34.5 g of ethanol to 500 g of water changes the freezing point of the solution. Use the freezing point depression constant of water as 2 K kg $$mol^{-1}$$ . The figures shown below represent plots of vapour pressure (V.P.) versus temperature (T). [molecular weight of ethanol is 46 g $$mol^{-1}$$] Among the following, the option representing change in the freezing point is
For the following cell, $$Zn(s)\mid ZnSO_{4}(aq)\parallel CuSO_{4}(aq)\mid Cu(s)$$ when the concentration of $$Zn^{2+}$$ is 10 times the concentration of $$Cu^{2+}$$, the expression for $$\triangle G$$ ((in J $$mol^{-1}$$) is [F is Faraday constant; R is gas constant; T is temperature; $$E^{0}(cell)=1.1V$$]
