While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the XY-plane containing two small holes that act as two coherent point sources (S₁, S₂) emitting light of wavelength 600 mm. The student mistakenly placed the screen parallel to the XZ-plane (for z > 0) at a distance D = 3 m from the mid-point of S₁S₂, as shown schematically in the figure. The distance between the source d = 0.6003 mm. The origin O is at the intersection of the screen and the line joining S₁S₂.


Which of the following is(are) true of the intensity pattern on the screen?

In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is (are) true?

Light of wavelength $$\lambda$$_ph falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $$\phi$$ and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de-Broglie wavelength of the electrons passing through the anode is $$\lambda$$_e, which of the following statement(s) is (are) true?

A frame of the reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity $$\omega$$ is an example of a non-inertial frame of reference. The relationship between the force $$\overrightarrow F $$_rot experienced by a particle of mass m moving on the rotating disc and the force $$\overrightarrow F $$_in experienced by the particle in an inertial frame of reference is,

$$\overrightarrow F $$_rot = $$\overrightarrow F $$_in + 2m ($$\overrightarrow v $$_rot $$\times$$ $$\overrightarrow \omega $$) + m ($$\overrightarrow \omega $$ $$\times$$ $$\overrightarrow r $$) $$\times$$ $$\overrightarrow \omega $$,

where, v_rot is the velocity of the particle in the rotating frame of reference and r is the position vector of the particle with respect to the centre of the disc.


Now, consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise with a constant angular speed $$\omega$$ about its vertical axis through its centre. We assign a coordinate system with the origin at the centre of the disc, the X-axis along the slot, the Y-axis perpendicular to the slot and the Z-axis along the rotation axis ($$\omega$$ = $$\omega$$ $$\widehat k$$). A small block of mass m is gently placed in the slot at r = (R/2)$$\widehat i$$ at t = 0 and is constrained to move only along the slot.

The distance r of the block at time t is