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
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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)
Semester Final Examination- 2017
Program: ME
Semester: Autumn 2017
Course Title: Coordinate geometry and
Matrices
Time: 2 hours Ttal Marks: 40
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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.
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