+3-I-S-NEP-Major-I-P-2-Sc-Phy

2024 | Full Marks : 100

PART-I Answer all the following Questions. | 1x 10

• The direction of coriolis force is radially __. (inward/outward/normal)
• Does the moment of Inertia is a scalar quantity ? (yes/ no/uncertain)
• The viscosity of liquid __ with rise of temperature.
• The gravitational field intensity inside spherical shell is __.
• The orbital velocity of geostationary satellite is __ .
• The damping force is directly proportional to __ and oppositely directed.
• Does the poiseullie’s formula valid during turbulent fluid flow ? (yes no/uncertain)
• The compressibility is reciprocal of __ of fluids.
• The kinetic energy of a particle moving with relativistic velocity is __ .
• Michelson Morley Experiment in 1887 were perfomed to detct the relative motion berween the earth and __.

PART-II | in 50 words each | 2 x 9

• State Routh Rule on moment of Inertia.
• Distingiish between centre of mass Frame and Laboratory frame.
• State and prove parallel axes theorem.
• Distinguish between streamline and turbulent flow.
• When a particle execute SHM along a straight line has veoeity $v_1$ and $v_2$ at positions $x_1$ and $x_2$ respectively. Obtain the frequeney of oscillation.
• With what velocity particle should move so that its mass appears to increase by 10% than of its rest mass.
• Prove that $E^2=p^2c^2+m_0^2c^4$ in relativistic mechanics.
• Notes on centrifugal furce.
• Define quality fctor and write its significance.

PART-III | each questions in 250 words | 5 x 8

• State and prove the conservation of angular momentum for a system of particles.
• Establish the Euler’s equations of motion for a rigid body.
• Derive the twisting torque expression for a solid cylinder.
• Obtain the velocity of gravity waves and ripples.
• Show that two body central force problem is equivalent to one body problem.
• Write a note on global positioning system (GPS).
• Discuss about relativistic transformation of velocity.
• Using Lorentz transformation show that $x^2+y^2+z^2=c^2t^2$ is invariant.
• Establish the laws of physics in uniformly rotating frame.
• Establish the theory of Kater’s Pendulum.

PART-IV | Answer any four of the following in 800 words each. | 8x4

1) Obtain the moment of Inertia of a Fly wheel. 2) Define various elastic constants and establish relations between them. 3) Under Central force motion deduce Kepler’s Laws of Planetary motion. 4) Write special theory of relativity. Deduce Lorentz transformation equations. 5) Deduce expression for gravitational potential and field due to a solid sphere at various locations.s locations.

###+3-I-S-CBCS(MS)-Sc(H)-Core-II-Phy-R&B

2023 | Full Marks : 60

PART-I | Answer the following questions. | 1x8

• The net momentum of center of mass frame is _____.
• _____ plays an important role in the formation of cyclone and its direction of rotation.
• The excess pressure inside the soap bubble in terms surface tension (T) is expressed as _____.
• The theoretical limit of Poisson’s ratio is from ___ to ___.
• Minimum number of satellite required to get tree dimensional position is __.
• The expression for reduced mass is __.
• The total energy in simple harmonic motion is expressed as _____.
• Relativistic momentum (P) and energy of a particle (E) are related as _____.

PART-II | Answer any eight within two to three sentences. | 1.5x8

• Write Euler’s equation.
• Define Routh?s rule.
• Find relation among torque and angular momentum.
• Define simple harmonic motion.
• Give two examples of center of force.
• Define surface tension.
• Define ripples.
• Define orbital velocity.
• What is meant by time dilation ?
• Write Einstein’s mass-energy relation and discuss its significance.

PART-III | Answer any eight of the following (in maximum 75 words. | 2x8

• State and prove perpendicular axis theorem.
• Explain pseudo force with an example.
• Define various elastic co-efficient.
• Why liquid drops are spherical in shape ?
• Distinguish between gravitational and inertial mass.
• Distinguish between streamline and turbulent flow.
• What is geosynchronous satellite ?
• A particle executing simple harmonic motion has maximum speed of30 cm/ sec and maximum acceleration of 60 cm/sq-sec. Calculate period of the oscillation.
• Describe sharpness of resonance.
• Write various features of central force of motion.

PART-IV | Answer within 500 words each. | 6×4

4) Derive expression of acceleration for uniformly rotating frame.

OR

Find expression for moment of inertia of a solid cylinder about its own axis.

5) Discuss various assumptions used to derive Poiseuille’s formula and derive it.

OR

What is cantilever ? Derive expression for the depression at the loaded end of single cantilever having negligible weight.

6) Derive expression for gravitational potential at both inside and outside points for a spherical shell.

OR

Define torsional rigidity. Derive its expression for a solid cylinder.

7) Solve the differential equation of a damped harmonic oscillator. Discuss overdamped, critically damped and underdamped cases.

OR

Derive Lorentz transformation equations

+3-I-S-CBCS(MS)-Sc(H)-Core-II-Phy-R&B

2022 | Full Marks : 60

PART-I | 1x8

• Write the Moment of Inertia of a sphere about an axis passing through its diameter.
• Write an expression for coriolis force.
• Which state of Matter posses only bulk modulus of elasticity.
• Write the dimension of coefficient of viscosity.
• Which quantity measures mass of a body ?
• A central force is a _____ force.
• For which Frame of Reference the postulates of special Theory of Relativity are applicable ?
• At which position the potential energy of a particle is equal to its kinetic energy while executing simple Harmonic motion ?

PART-II | Answer any eight within two to three sentences | 1.5x8

• What is Laboratory frame of reference ?
• What do you mean by Rigid body ?
• What is fictitious Force ? Give one example.
• Define Bending Moment.
• How surface Tension of liquid varies with temperature and pressure.
• What is capillarity. Give one example.
• What is Weightlessness ?
• What is Resonance ? Give one example.
• Write Relation between Frequency and Wave number.
• What is Central Force Field ?

PART-III | Answer any eight of the following (in maximum 75 words.) | 2x8

• State perpendicular axes Theorem of Moment of Inertia.
• Explain uniformly rotating frame with examples.
• What force is reauired to stretch a steel Wire of 0.5cm$^2$ in cross section to double its length ?(Given $Y=2 \times 10^{11}N/m^2$)
• Distinguish between ‘g’ and ‘G’. Write relation between them.
• Distinguish between gravity waves and ripples.
• Write the basic features of geostationary satellites.
• Calculate the displacement to amplitude ratio for a S.H.M., when kinetic Energy is 90% of total energy.
• Explain power dissipation of damped Harmonic oscillations.
• Explain, particles of zero rest mass.
• Explain Mass - Energy equivalence.

PART-IV | Answer within 500 words each | 6×4

4) Define torque and Angular momentum. Then derive an expression for Euler’s equation of rotation of a rigid body about a fixed point.

OR

Explain coriolis force. Derive an expression for it.

5) Define young’s Modulus of elasticity (y), Bulk Modulus of elasticity (k) and Modulus of Rigidity ($\eta$). Then find relation between them.

OR

Define coefficient of viscosity. Then derive an expression for poiseuille’s equation of flow of liquid

6) Establish the differential equation of motion of a particle under a central force and deduce its solution for attractive inverse square force field.

OR

Define gravitational potential. Then derive an expression for the gravitational potential at a point. (i) outside (ii) on the surface of a solid sphere.

7) Define S.H.M. Then derive an expression for total energy of a particle executing S.H.M. with graphical representation.

OR

Write Lorentz Transformation equations. Then using Lorentz Transformation equations derive an expression for Relativistic addition of velocities.