Date : 10/06/2024
The Institution of Engineers, Bangladesh
AMIE SECTION "A" (OLD & NEW) EXAMINATION, APRIL 2024
Sub : Physics
Full Marks : 100
Time : 3 Hours
The figures in the margin indicate full marks.
There are SEVEN questions in this paper. Answer any FIVE.
Question 1
(a)
State the basic assumptions of the kinetic theory of gases.
4
(b)
Applying the principle of kinetic theory of gases, show that the pressure exerted by a perfect gas is equal to two-thirds of the kinetic energy of the molecules per unit volume.
12
(c)
Calculate the kinetic energy of hydrogen per gram-molecule at $0^{\circ}\text{C}$. The gas constant $R = 8.3 \times 10^{7}\text{ ergs/gm-mol}$.
4
Question 2
(a)
What is efficiency of an engine?
3
(b)
Derive an expression for the efficiency of a Carnot engine in terms of the temperatures of the source and the sink.
13
(c)
A Carnot engine whose temperature of the source is $127^{\circ}\text{C}$ takes $200\text{ calories}$ of heat at this temperature and rejects $150\text{ calories}$ of heat in the sink. Calculate the efficiency of the engine.
4
Question 3
(a)
Define simple harmonic motion with examples.
3
(b)
Show that, for a body executing simple harmonic motion, mechanical energy remains conserved. At what particular displacement is its energy, on average, half kinetic and half potential in form?
13
(c)
A body is vibrating with simple harmonic motion of amplitude $15\text{ cm}$ and frequency $4\text{ Hz}$. Compute the acceleration and velocity when the displacement is $9\text{ cm}$.
4
Question 4
(a)
Distinguish between traveling waves and stationary waves.
4
(b)
Show analytically that when a progressive wave is reflected from a rigid boundary, a stationary wave is produced. Show that the positions of nodes are independent of time.
12
(c)
The equation of a transverse wave along a string is given by the relation:
$$y = 0.02 \sin(30t - 4.0x)$$
where $t$ is in seconds and $x$ in meters. Find
(i) frequency, and
(ii) speed of the wave.
4
Question 5
(a)
What do you mean by a capacitor and capacitance?
4
(b)
Obtain the expressions of capacitance for a:
(i) Spherical capacitor of radii '$a$' and '$b$',
(ii) Parallel plate capacitor with dielectric constant '$K$'.
12
(c)
A parallel plate capacitor has plates of area $0.1\text{ m}^2$ separated by a distance of $0.02\text{ m}$. The plates are covered by a dielectric material of constant $5$. Calculate the capacitance of the capacitor.
4
Question 6
(a)
State and explain Ampere's law.
4
(b)
A flat strip of copper of width '$a$' and negligible thickness carries a current '$i$'. Find the magnetic field at a distance '$R$' from the center of the strip, at right angles to the strip.
12
(c)
The flux linking in an air-cored coil of $500\text{ turns}$ changes from $30\text{ to }60\text{ }\mu\text{Wb}$ in $2\text{ ms}$. Calculate the value of the electro-motive force induced in the coil.
4
Question 7
(a)
What are Newton's rings? Explain their formations.
4
(b)
Describe how you would use these rings to measure the wavelength of a monochromatic light. Derive the formula used.
12
(c)
Newton's rings are formed by light reflected normally from a combination of a plano-convex lens and a glass surface. The diameters of two successive dark rings are $2.0\text{ mm}$ and $2.236\text{ mm}$. The wavelength of light is $5.9 \times 10^{-5}\text{ cm}$. Find the radius of curvature of the lens.
4
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