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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