Instructions

For the following questions answer them individually

Question 21

An ideal gas undergoes a four step cycle as shown in the 𝑃−𝑉 diagram below. During this cycle, heat is absorbed by the gas in

Question 22

An extended object is placed at point O, 10 cm in front of a convex lens $$L_1$$ and a concave lens $$L_2$$ is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are 20 cm. The refractive index of both the lenses is 1.5. The total magnification of this lens system is

Question 23

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

Instructions

Question Stem

A projectile is thrown from a point O on the ground at an angle $$45^\circ$$ from the vertical and with a speed $$5\sqrt{2}$$ m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, 0.5 s after the splitting. The other part, 𝑡 seconds after the splitting, falls to the ground at a distance 𝑥 meters from the point O. The acceleration due to gravity $$g = 10 m/s^2$$.

Instructions

Question Stem

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes $$q_1 \mu C$$. Then S is switched to position Q. After a long time, the charge on the capacitor is $$q_2 \mu C$$.

Instructions

Question Stem

Two point charges $$−Q$$ and $$+ \frac{Q}{\sqrt{3}}$$ are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius 𝑅 and potential 𝑉=0 in the xy-plane with its center at (b, 0). All lengths are measured in meters.

Instructions

For the following questions answer them individually

Question 30

A horizontal force 𝐹 is applied at the center of mass of a cylindrical object of mass 𝑚 and radius 𝑅, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is $$\mu$$. The center of mass of the object has an acceleration 𝑎. The acceleration due to gravity is 𝑔. Given that the object rolls without slipping, which of the following statement(s) is(are) correct?