Rotational Dynamics | Assignments

Assignment 1:

1. Three mass points $m_1$, $m_2$ and $m_3$ are located at the vertices of an equilateral triangle of length $a$. What is the moment of inertia of the system about an axis along the altitude of the triangle passing through $m_1$?

2. Four particles of masses $4\;kg$, $2\;kg$, $3\;kg$ and $5\;kg$ are respectively located at the four corners $A$, $B$, $C$ and $D$ of a square of side $1\;m$. Calculate the moment of inertia of the system about:

(i) an axis passing through the point of intersection of the diagonals and perpendicular to the plane of the square,

(ii) the side $AB$,

(iii) the diagonal $BD$.

Assignment 2:

3. A wheel is rotating at a rate of 1000 rpm & its kinetic energy is $10^6$ J. Determine the moment of inertia of the wheel about its axis of rotation.

4. Find (i) the radius of gyration & (ii) the MI of the rod of mass $100\; gm$ and length $100 \; cm$ about an axis passing through its center & perpendicular to its length.

5. Calculate the angular momentum of the earth rotating about its own axis. Mass of the earth is $5.98 * 10^{24}\; kg$, Mean radius of earth is $6.37 * 10^6\; m$, MI of the earth is $\frac{2}{5}MR^2$.

6. The moment of inertia od the wheel is $1000\; kgm^2.$ At a given instant, its angular velocity is $10 \; rad/s$. After the wheel rotates through an angle $100$ radians, the wheels angular velocity is $100\; rad/s$. Calculate (i) the torque applied on the wheel. (ii) the increase in rotational KE.

7. A ballet dancer stretches her arms to reduce her motion. Explain.

8. If earth contracts to half its radius, what would be the length of the day?

9. Explain why spokes are fitted in the cycle wheel.

10. A fan with blades takes longer time to come to rest than without the blades. Why?

11. If the earth is struck by meteorites, the earth will slow down slightly. Why?

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Heating Effect of Current | Grade XII | Part - 2

 

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Scalar and Vector | Assignment

Assignment 1:

1. If $B$ is added to $A$, under what condition does the resultant vector have a magnitude equal to $A + B$? Under what conditions are the resultant vector equal to zero?

2. State triangle law of vector addition. Obtain an expression for the resultant of two vectors $P$ and $Q$ inclined at angle $\theta$.

 

3. State the parallelogram law of vector addition. Derive the magnitude and direction of the resultant vector.

4. Can the sum of two equal vectors be equal to either of the vectors? Explain.

Assignment 2:

 

1. If the scalar product of two vectors is equal to the magnitude of their vector product, find the angle between them.

 

2. The magnitude of two vectors are equal and the angle between them is $\theta$. Show that their resultant divides angle $\theta$ equally. 

 

3. If B is added to A, under what condition does the resultant vector have a magnitude equal to A + B? under what conditions is the resultant vector equal to zero.

 

4. Two vectors $\vec{A}$ and $\vec{B}$ are such that $\vec{A} - \vec{B} = C$ and $A - B = C$. Find the angle between them.

5. If  $\widehat{i}$, $\widehat{j}$ and $\widehat{k}$ are unit vectors along $x, y,z - $ axis respectively. Find $\widehat{i}$ . ($\widehat{j}$ $\times$ $\widehat{k}$).

6. A force (in Newton) expressed in vector notation as $\vec{F} = 2 \widehat{i} + \widehat{j} - 3 \widehat{k}$ is applied on a body so that the displacement produced in meter is given by $\vec{D} = \widehat{i} - 2 \widehat{j} - 3 \widehat{k}$. Express the result and nature of the work done.

7. Given two vectors $\vec{A} = 4 \widehat{i} + 3 \widehat{j}$ and $\vec{B} = 5 \widehat{i} - 2 \widehat{j}$. Find the magnitude of each vector.

8. Can the walking of the person be an example of resolution of vector?

9. Show that the flight is an example of composition of vectors.

10. Find the unit vector of  $3 \widehat{i} + 7\widehat{j} - \widehat{k}$

 

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Physical Properties | Assignment Collection

1) Find the dimension formula of,

            Density / Pressure / Work / Energy / Power / Gravitational Constant / Momentum ?

2) To find the time period of a simple pendulum, its time period (t) may depend upon (i) mass (m) of the pendulum (ii) the length (l) and (iii) acceleration due to gravity (g).

3) Convert 1 dyne into Newton.

4) Convert 500 erg into Joule.

5) Find the dimensions of the constants $a$ and $b$ in the Vander Waal's equation of state of a real gas 

Direct Current Circuit | Assignment Collection

Assignment 1

1. Define $1 \; \;  Ampere$ current. 

2. Describe the mechanism of metallic conduction. 

3. Show that one ampere is equivalent to a flow of $6.25 ∗ 10^{18}$ elementary charges per second. 

4. How many electrons pass through a lamp in one minute, if the current is $300\;  mA$? 

5. How many electrons per second flow through a filament of a $120 \; V$ and $60 \; W$ electric bulb? Given electric power is the product of voltage and current. 

6. The amount of charge passing through cross-section of a wire is $q(t) = at^2 + bt + c $

•     Write the dimensional formulae for a, b, c.
•     If the values of a, b and c in SI units are 5, 3, 1 respectively, find the value of current at $t = 5$ second.

Assignment 2

1. Define drift velocity and current density. Establish a relation between drift velocity of electrons and current density in the conductor. 

2. Define Ohm’s Law and discuss the experimental verification of Ohm’s law. (Only for section A) 

3. A copper wire has a diameter of $1.02 \; mm$ and carries a constant current of $1.67 \; A$. If the density of free electrons in copper is $8.5 ∗ 10^{28}/m^3$, calculate the current density and the drift velocity of the electrons. [Ans: $J = 2.04 ∗ 10^6 \; A/m^2$; $V_d = 1.5 ∗ 10^{-4}\; m/s$] 

4. A copper wire has a resistance of $10 \; \Omega$ and an area cross-section $1 \; mm^{2}$. A potential difference of $10 \; V$ exists across the wire. Calculate the drift speed of electrons if the number of electro per cubic meter in copper is $ 8 ∗ 10^{28}$ electrons. [Ans: $0.078 \;  mm/s $]

Assignment 3

1. Resistance of a wire of length $1\;m$, diameter $1\;mm$ is $2.2\; \Omega$. Calculate its resistivity and conductivity. [Ans: $\rho = 1.727 \; * \; 10^{-6}\; \Omega \;m$;   $5.79 * 10^ {-5} \; \Omega^{-1}\; m^{-1}$]

2. Two wires, one of copper and another of iron, have the same diameter and carry the same current. In which wire the drift velocity of electrons will be more?

3. A wire is stretched to double its length. What happens to its resistance and resistivity?

4. A wire having a diameter of $1.2 \; mm$ and resistivity of $100 * 10^{-8} \Omega \; m$ at $0^{0}C$ is connected across a cell of emf $1.5\;V$ and gives a current of $10\;mA$. Calculate the length of the wire. [Ans: $  169.6\;m $]

Assignment 4

1. Determine the voltage drop across the resistor $R_1$ in the circuit given below with $V = 60\;V$, $R_1 = 18\;Ohm$, $R_2 = 10\;Ohm$ [Answer = $45\; V$]

2. Two resistors of resistance $1000\; \Omega$ and $2000 \; \Omega$ are joined in series with a $100\; V$ supply. A voltmeter of internal resistance $4000 \; \Omega$ is connected to measure the potential difference across $1000 \; \Omega$ resistor. Calculate the reading shown by the voltmeter. [Answer: $28.57\; Volt$]

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