Header Ads

Physics and Math - Semester final question

 Department Of Mechanical Engineering
Semester Final Examination- 2017
Program: ME
Semester: Autumn 2017
Course Title: Physical Optics and Wave and Oscillation
Course Code: PHY 4201

Time: 2 hours        Ttal Marks: 40

Part A
(Answer Any Two Out of Three)
1.       Prove that, the average potential energy of a body executing simple harmonic motion is half of its total energy.
2.       Derive the equation of the resultant vibration in the Fraunhofer diffraction by a single slit.
3.       Derive the equation of the displacement of simple harmonic motion.

Part B
(Answer Any Four Out of Six)
1.       A spring, hung vertically, is found to be stretched by 0.06m from its equilibrium position when a force of 12 N acts on it. Then a 6 Kg body is attached to the end of the spring and is pulled 0.12 m from its equilibrium position along the vertical line. The body is then released and it executes simple harmonic motion.
a.       What is the force constant of the spring?
b.       What is the maximum velocity of the oscillating body?
c.       What is the mechanical energy of the oscillating body?

2.       A light of wavelength 5400A.U is incident normally on a plane diffraction grating having 18000 lines per inch. How many orders of diffracted image can be observed?

3.       A spring hung vertically is found to be stretched by 0.1 m from its equilibrium position when a force of 20 N acts on it. Then a 10 Kg body is attached to the end of the spring and is pulled 0.2 m from its equilibrium position along the vertical line. The body is then released and it executes simple harmonic motion. What is the displacement of the body as function of time?

4.       The limits of the visible spectrum are approximately 4000 A.U and 7000 A.U. Find the anguler breadth of the third order visible spectrum produced by plane diffraction grating having 12000 lines per inch when light is incident normally on the grating.


5.       The displacement of an oscillating particle as instant is given by
y = A Sin wt + B Cos wt
Prove that, it is executing a simple harmonic motion


6.       In a Fraunhofer diffraction, due to narrow slit of width 0.04 cm, the screen is placed 4 m away from lens used to obtain the pattern. If the second maxima lie 10 mm on either side of the central maxima, Find the wavelength of light used. (for second maxima B= 2.46r)



 Department Of Mechanical Engineering
Semester Final Examination- 2017
Program: ME
Semester: Autumn 2017
Course Title: Coordinate geometry and Matrices
Course Code: MATH- 4101
Download Link
Time: 2 hours        Ttal Marks: 40
Instruction:
i.                     Answer any four questions from the following.
ii.                   Figures in the right margin indicate full marks
iii.                 Part of the same question are to be answered consecutively.
iv.                 Answer to each question should be started from a new page.
Question:
1.       i. Find the equation of the plane through the points ( 2,2,1) and (9,3,6) and perpendicular to the plane 2x + 6y + 6z = 9                         5.
ii. Find the equation of a line which passes through the point (3,4) and makes intercepts on the axes equal in magnitude but opposite in sign.                                    5
2.       i. Find the equation of the plane through the points (2, 3,1), (1,1,3) and (2,2,3). Find also the perpendicular distance from the point (5,6,7) to this plane                         6.
ii. Find the equation of the line passing through (-3,-4P and
a.       parallel to x-axis. b. parallel to y-axis
3.       i. A point P moves at a fixed distance of 8 units from a given point A(-2, 5). Find the locus of P. Verify whether the point B(6,5) also lies on the locus or not.
ii. Determine the slope and the y intercept of the line whose equation is 8x + 3y = 5
4.       i. The segment of line, intercepted between the coordinate axes is bisected at point (x1, y1). Find the equation of the line.
ii. Show that the point (-1,0, -4), (0,1,-6) and (1,2,-5) from a right angled triangle.
5.       i. Prove that the points (2,2,2), (-4,8,2) and (4,4,10) are vertices of square.
ii. Show that triangle formed by the points (-2, 4, -3), (4,-3,-2) and (-3, -2, 4) is equilateral.

No comments

Powered by Blogger.