# Joint Entrance Screening Test (JEST) Past Year Question Papers 2020 Part 4

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Q 10. Consider a cube (see figure) of volume V containing N molecules each of mass m with uniform density . Suppose this system is equivalent to a system of M noninteracting gases such that molecules of the ith gas are in number, each with an identical y -component of velocity . What is the pressure P on the surface of area a?

(a)

(b)

(c)

(d)

Q 11. The wave function of a particle subjected to a spherically symmetric potential is given by . Which one of the following statements is true about ?

(a) It is an Eigen function of with

(b) It is an Eigen function of with

(c) It is an Eigen function of with

(d) It is not an Eigen function of

Q 12. The Hamiltonian for a particle of mass m is given by , where is a nonzero constant. Which one of the following equations is correct?

(a)

(b)

(c)

(d)

Q 13. A continuous He-Ne laser beam is ‘chopped’ , using a spinning aperture into square pulses. The order-of-magnitude estimate of the spectral width of the emerging ‘pulsed’ light is

(a)

(b)

(c)

(d)

Q 14. The Hamiltonian of a classical particle is given by . Given

t is a constant of motion (where ) . What is the value of ?

(a)

(b) 0

(c) 1

(d)

Q 15. Three polarizers are stacked, normal to a central axis, along which is incident a beam of unpolarized light of intensity . The first and the third polarizers are perpendicular to each other and the middle polarizer is rotated at an angular frequency about the central axis (light beam) . The time dependent intensity of light emerging after the third polarizer will be given by

(a)

(b)

(c)

(d)

## PART C: 3- Mark Numerical Questions

Q 1. A thin film of water having refractive index floats on the surface of a beaker of silicone oil having refractive index . The arrangement is illuminated by 600 nm light incident normally from top and a large region of the film appears bright red. What is the minimum possible thickness of the film (in nm) ?

Q 2. What is the value of the following integral?

Q 3. Two compartments in a cylinder with uniform cross section and total length 102 cm are separated by a sliding partition, which can move but does not allow heat to pass across it.

No molecules are present in either of the compartments. The radiation inside each compartment is in thermal equilibrium with its walls. The walls at the two ends of the cylinder are maintained at temperatures 2000 K and 4000 K, respectively. The sides are perfectly insulated. Find the location of the partition, measured from the left end of the container.

Q 4. A laser has output power of 150 mW with beam diameter of 2 mm at a wavelength 630 nm.

What is the value of the electric field in units of is? Use Coulomb՚s constant,

Q 5. A two-state quantum system has energy eigenvalues corresponding to normalized states . At time t = 0 the system is in the quantum state . Find the probability that the system will be in the same state at time , where h is the

Q 6. A small insect of mass m is sitting on the rim of a uniform circular horizontal disk of radius R and mass M. The system is rotating at a constant angular velocity about a frictionless vertical axis passing through the center of the disk. The insect started to crawl towards the center of the disk. Assume , and let the final angular velocity of the system, when the insect reaches the centre of the disk be . What is the value of

Q 7. A particle is moving on a one-dimensional discrete lattice with lattice spacing unity. It can move from a site to its nearest neighbour site every seconds with p being the probability to move right and being the probability to move left. Consider that the particle starts at origin, x = 0 at time t = 0. Taking , calculate the variance at time seconds, where (x) is the average position.

Q 8. Analyse the op-amp circuit shown in the figure below. What is the output voltage in millivolts if and ?

Q 9. Some bacteria are added to a bucket at time 10 am. The number of bacteria doubles every minute and reaches a number at 10: 18 am. How many seconds after 10 am were there bacteria?

Q 10. A cleaning machine presses a circular mop of radius R = 30 cm vertically down on a floor with a total force and rotates it with a constant angular speed about the vertical axis passing through the centre of mop. If the force is distributed uniformly over the mop and if the coefficient of friction between the mop and the floor is , what is the value of torque in N - cm applied by the machine on the mop?