# Joint Entrance Screening Test (JEST) Past Year Question Papers 2019 Part 5

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## PART C: 3-Mark Numerical Questions

Q1. A thin uniform steel chain is 10m long with a linear mass density of 2kg. The chain hangs vertically with one end attached to a horizontal axle, having a negligibly small radius compared to its length. What is the work done (in N-m) to slowly wind up the chain on to the axle? The acceleration due to gravity is .

Q2. A one-dimensional harmonic oscillator is in the state where is the normalized energy Eigen state with eigenvalue . Let the expectation value of the Hamiltonian in the state be expressed as . What is the value of ?

Q3. The Euler polynomials are defined by

What is the value of ?

Q4. What is the angle (in degrees) between the surfaces and at the point

Q5. Consider a system of 15 non-interacting spin-polarized electrons. They are trapped in a two dimensional isotropic harmonic oscillator potential . The angular frequency is such that in some chosen unit. What is the ground state energy of the system in the same units?

Q6. Consider the motion of a particle in two dimensions given by the Lagrangian

where . The initial conditions are given as meters, .

What is the value of seconds in meters?

Q7. A diatomic ideal gas at room temperature is expanded at a constant pressure . If the heat absorbed by the gas is Q = 14 Joules, what is the maximum work in Joules that can be extracted from the system?

Q8. An optical line of wavelength in the spectrum of light from a star is found to be red shifted by an amount of . Let v be the velocity at which the star is receding. Ignoring relativistic effects, what is the value of ?

Q9. In the Young՚s double slit experiment (screen distance D = 50cm and d = 0.1cm) , a thin mica sheet of refractive index n = 1.5 is introduced in the path of one of the beams. If the central fringe gets shifted by 0.2, what is the thickness (in micrometer) of the mica sheet?

Q10. A circular metal loop of radius a = 1m spins with a constant angular velocity rad/s in a magnetic field B = 3 Tesla, as shown in the figure. The resistance of the loop is 10 Ohms. Let P be the power dissipated in one complete cycle. What is the value of in Watts?