# Joint Entrance Screening Test (JEST) Past Year Question Papers 2018 Part 4

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## PART C (THREE MARKS QUESTIONS)

Q1. An ideal fluid is subjected to a thermodynamic process described by and where is energy density and *P* is pressure. For what values of *n* and the process is adiabatic if the volume is changed slowly?

(a)

(b)

(c) )

(d) )

Q2. If *y* (*x)* satisfies

and for they is

(a) 0

(b) 1

(c)

(d) Infinity

Q3. A frictionless heat-conducting piston of negligible mass and heat capacity divides a vertical, insulated cylinder of height 2*H* and cross sectional area *A* into two halves.

Each half contains one mole of an ideal gas at temperature and pressure corresponding to STP. The heat capacity ratio is given. A load of weight *W* is tied to the piston and suddenly released. After the system comes to equilibrium, the piston is at rest and the temperatures of the gases in the two compartments are equal.

What is the final displacement *y* of the piston from its initial position, assuming ?

(a)

(b)

(c)

(d)

Q4. An apparatus is made from two concentric conducting cylinders of radii *a* and *b* respectively, where *a* < *b*. The inner cylinder is grounded and the outer cylinder is at a positive potential *V*. The space between the cylinders has a uniform magnetic field *H* directed along the axis of the cylinders. Electrons leave the inner cylinder with zero speed and travel towards the outer cylinder. What is the threshold value of *V* below which the electrons cannot reach the outer cylinder?

(a)

(b)

(c)

(d)

Q5. A theoretical model for a real (non-ideal) gas gives the following expressions for the internal energy (*U)* and the pressure (*P)* , and where *a* and *b* are constants. Let and be the initial volume and initial temperature respectively. If the gas expands adiabatically, the volume of the gas is proportional to

(a) *T*

(b)

(c)

(d)

Q6. Consider two coupled harmonic oscillators of mass *m* in each. The Hamiltonian describing the oscillators is

The eigenvalues of are given by (with and being non-negative integers)

(a)

(b)

(c)

(d)

Q7. A ball comes in from the left with speed 1 (in arbitrary units) and causes a series of collisions. The other four balls shown in the figure are initially at rest. The initial motion is shown below (the number in the circle indicate the object՚s relative mass) . These initial velocities of the balls shown in the figure are represented as

A negative sign means that the velocity is directed to the left. All collisions are elastic.

Which of the following indicates the velocities of the balls after all the collisions are completed?

(a)

(b)

(c)

(d)

Q8. Consider the Lagrangian

of a particle executing oscillations whose amplitude is *A*. If *p* denotes the momentum of the particle, then is

(a)

(b)

(c)

(d)

Q9. A block of mass *M* rests on a plane inclined at an angle with respect to the horizontal.

A horizontal force is applied to the block If is the static friction between the block and the plane, the range of so that the block remains stationary is

(a)

(b)

(c)

(d)

Q10. The coordinate *q* and the momentum *p* of a particle satisfy

If *A* (*t)* is the area of any region of points moving in the (*q*, *p)* -space, then the ratio is

(a) 1

(b)

(c)

(d)