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Physics Resource CenterDate : 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)
4
State the basic assumptions of the kinetic theory of gases.
(b)
12
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.
(c)
4
Calculate the kinetic energy of hydrogen per gram-molecule at $0^{\circ}\text{C}$. The gas constant $R = 8.3 \times 10^{7}\text{ ergs/gm-mol}$.
Question 2
(a)
3
What is efficiency of an engine?
(b)
13
Derive an expression for the efficiency of a Carnot engine in terms of the temperatures of the source and the sink.
(c)
4
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.
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Question 3
(a)
3
Define simple harmonic motion with examples.
(b)
13
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?
(c)
4
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 $9\text{ cm}$.
Question 4
(a)
4
Distinguish between group velocity and phase velocity.
(b)
12
Obtain an expression for a plane progressive wave travelling in the positive $x$-direction.
(c)
4
A 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.
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Question 5
(a)
4
What do you mean by a capacitor and capacitance?
(b)
12
Obtain the expressions of capacitance for a:
(i)
Spherical capacitor of radii '$a$' and '$b$'.
(ii)
Cylindrical capacitor of length '$l$' formed by two coaxial cylinders of radii '$a$' and '$b$'.
(c)
4
A plane-parallel capacitor has circular plates of radius $10\text{ cm}$, separated by a distance $1.0\text{ mm}$. How much charge is stored on each plate when their electric potential difference has the value of $100\text{ V}$?
Question 6
(a)
4
State and explain Ampere's law.
(b)
12
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.
(c)
4
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.
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Question 7
(a)
4
Differentiate between constructive and destructive interference of light.
(b)
12
Describe the theory of Newton's rings to determine the radius of curvature of a plano-convex lens.
(c)
4
Newton's rings are formed with sodium light between a plane glass plate and a convex lens 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.
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