Solve your IGNOU Doubts

Question:

The maximum speed with which a $1000\text{ kg}$ car can make a turn in a circular path is $15.0\text{ ms}^{-1}$ . The radius of the circle in which the car is turning is $30.0\text{ m}$ . Determine the force of friction being exerted upon the car and the coefficient of friction between the car and the road. Take $g = 10.0\text{ms}^{-1}$ .

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Question:

$\frac{d^2y}{dx^2} + 11 \frac{dy}{dx} + 24y = 0$

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Question:

$(x + 1) \frac{dy}{dx} = (2e^{-y} - 1); \text{ } y(0) = 1$

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Question:

A curve is described by the following parametric equations
$x = 2 \cos t, y = 2 \sin t, z = \cos(3t)$
Determine the unit tangent vector to the curve at the point $t = \frac{\pi}{2}$ .

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Question:

Three vectors $\mathbf{\vec{a}}$ , $\mathbf{\vec{b}}$ and $\mathbf{\vec{c}}$ satisfy the condition $\mathbf{\vec{a}} + \mathbf{\vec{b}} + \mathbf{\vec{c}} = \mathbf{\vec{0}}$ . If $|\mathbf{\vec{a}}| = 4, |\mathbf{\vec{b}}| = 2$ and $|\mathbf{\vec{c}}| = 3$ determine the value of $\mathbf{\vec{a}} \cdot \mathbf{\vec{b}} + \mathbf{\vec{b}} \cdot \mathbf{\vec{c}} + \mathbf{\vec{c}} \cdot \mathbf{\vec{a}}$ .

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Question:

A uniform plane wave of $100\text{ MHz}$ travelling in free space strikes a large block of a material having $\varepsilon = 9\varepsilon_0$ , $\mu = 4\mu_0$ and $\sigma = 0$ normal to the surface. If the incident electric field vector is given by
$$\vec{E} = 1000\cos(\omega t - \beta y)\hat{z}\text{ Vm}^{-1}$ $
write the complete expressions for the incident, reflected and transmitted field vector

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Question:

Using Maxwell's equations in free space, derive the wave equation for the x-component of the electric field vector.

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Question:

Discuss the B-H curve for a ferromagnet.

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Question:

Using Biot-Savart's law, obtain an expression for the magnetic field due to electric current flowing in a long straight wire at a distance R from the wire along a line perpendicular to the wire.

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Question:

The number density of electrons in the aluminium metal is $9.64 \times 10^{28}\text{ m}^{-3}$ . Calculate the drift velocity of electrons in a aluminium wire of cross-sectional area $2.0\text{ mm}^2$ in which a current of 4 A is flowing.

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Question:

What do you understand by linear conductors? Discuss the conditions under which metals do not behave as linear conductors.

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Question:

hree capacitors are connected to each other as shown below:

Image ignouassignments-ignouacademy-com--p-your-48492

Calculate the equivalent capacitance between points A and B.

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Question:

State Gauss’s Law. What does spherically symmetric charge distribution mean? Use Gauss’s Law to determine the electric field of a solid metallic sphere of radius R having volume charge density $\rho$ at a point outside the sphere.

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Question:

Two positively charged particles having charges $10\text{ }\mu\text{C}$ and $-5\text{ }\mu\text{C}$ , respectively, are kept at a distance of $1\text{ m}$ from each other. Determine the force on each charge and the electric field due to each charge. Show the force and electric field vectors on appropriate diagrams. What is the resultant force at a point midway from the two charges along the straight line joining them?

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Question:

Calculate the flux of a vector field $\vec{F} = 2x\hat{i} + y\hat{j} + 3z\hat{k}$ through the surface of a cube defined by $0 \le x \le 2 ; 0 \le y \le 2 ; 0 \le z \le 2$ .

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Question:

Calculate the net work done by a force $\vec{F} = (6x - 2y)\hat{i} + (x^2)\hat{j}$ in taking a particle along the straight line between the points (5, -3) to (0,0) and then along the straight line between the points (0,0) to (5,3). Is the force conservative? Explain.

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Question:

Consider a rigid body rotating about a fixed axis with a constant angular velocity $\vec{\omega}$ , directed along the axis of rotation. The velocity $\vec{v}$ of a particle on the rigid body is $\vec{\omega} \times \vec{r}$ . Calculate $\vec{\nabla} \times \vec{v}$ .

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Question:

The height of a hill is given by $z = 100 - x^2 y^2$ . Calculate the maximum rate of change (also called the steepest ascent) in the height of the hill at the point (2,1). What is its direction?

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Question:

What is Fermi-energy? Obtain an expression for Fermi energy for a system of N Fermions enclosed in a volume V. What will be the value of Fermi-energy (in eV) of gold at Fermi-temperature $6.42 \times 10^4 K$ ?

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Question:

Using the Planck's radiation law:
$$u_\lambda d\lambda = \frac{8\pi hc}{\lambda^5} \left( \frac{1}{\exp \left( \frac{hc}{\lambda k_B T} \right) - 1} \right) d\lambda \text{ , deduce (i) Rayleigh-Jean's law, (ii) Wien's law}$
and (iii) Stefan's law. (10)