Verify Lagrange's mean-value theorem for the following function:
Question: Verify Lagrange's mean-value theorem for the following function: $f(\mathrm{x})=\log \mathrm{x}$ on $[1, \mathrm{e}]$ Solution:...
Read More →A current of 2A enters at the corner d of a square frame abcd of side 20cm
Question: A current of $2 \mathrm{~A}$ enters at the corner $\mathrm{d}$ of a square frame abcd of side $20 \mathrm{~cm}$ and leaves at the opposite corner b. A magnetic field $B=0.1 \mathrm{~T}$ exists in the space in a direction perpendicular to the plane of the frame as shown in figure. Find the magnitude and direction of the magnetic forces on the four sides of the frame. Solution:...
Read More →Consider a 10cm long portion of a straight wire carrying
Question: Consider a $10 \mathrm{~cm}$ long portion of a straight wire carrying a current of $10 \mathrm{~A}$ placed in a magnetic field of $0.1 \mathrm{~T}$ making an angle of $53^{\circ}$ with the wire. What magnetic force does the wire experience? Solution:...
Read More →Verify Lagrange's mean-value theorem for the following function:
Question: Verify Lagrange's mean-value theorem for the following function: $f(x)=x^{2 / 3}$ on $[0,1]$ Solution:...
Read More →When a proton is released from rest in a room,
Question: When a proton is released from rest in a room, its starts with an initial acceleration $a_{0}$ towards west. When it is projected towards north with a speed $v_{0}$, it moves with an initial acceleration $3 \mathrm{a}_{0}$ towards west. Find the electric field and the maximum possible magnetic field in the room. Solution:...
Read More →A 10g bullet having a charge of
Question: A $10 \mathrm{~g}$ bullet having a charge of $4.00 \mu C$ is fired at a speed of $270 \mathrm{~m} / \mathrm{s}$ in a horizontal direction. A vertical magnetic field of $500 \mu T$ exists in the space. Find the deflection of the bullet due to the magnetic field as it travels through $100 \mathrm{~m}$. Make appropriate approximations. Solution:...
Read More →Verify Lagrange's mean-value theorem for the following function:
Question: Verify Lagrange's mean-value theorem for the following function: Solution: $\Rightarrow c=\log _{e}(e-1)$...
Read More →An experiment's diary reads as follows:" a charged particle is projected in a magnetic field of
Question: An experiment's diary reads as follows:" a charged particle is projected in a magnetic field of $(7.0 \vec{\imath}-3.0 \vec{\jmath}) \times 10^{-3} \mathrm{~T}$. The acceleration of the particle is found to be $(\vec{\imath}+7.0 \vec{\jmath}) \times 10^{-6} \mathrm{~m} / \mathrm{s}^{2 n}$. The number to the left $\bar{i}_{\text {in }}$ the last expression was not readable. What can this number be? Solution:...
Read More →Verify Lagrange's mean-value theorem for the following function:
Question: Verify Lagrange's mean-value theorem for the following function: $f(x)=(x-4)(x-6)(x-8)$ on $[4,6]$ Solution: Given:...
Read More →A magnetic field of
Question: A magnetic field of $\left(4.0 \times 10^{-3} \vec{k}\right)$ T exerts a force of $(4.0 \vec{\imath}+3.0 \vec{\jmath}) \times 10^{-10} \mathrm{~N}$ on a particle having a charge of $1.0 \times 10^{-9} \mathrm{C}$ and going in the $X-Y$ plane. Find the velocity of the particle. Solution:...
Read More →An electron is projected horizontally with a kinetic energy of
Question: An electron is projected horizontally with a kinetic energy of $10 \mathrm{keV}$. A magnetic field of strength $1.0 \times 10^{-7} \mathrm{~T}$ exists in the vertically upward direction. (a) Will the electron deflect towards right or towards left of its motion? (b) Calculate the sideways deflection of the electron in travelling through $1 \mathrm{~m}$. Make appropriate approximations. Solution:...
Read More →Verify Lagrange's mean-value theorem for the following function:
Question: Verify Lagrange's mean-value theorem for the following function: $f(x)=x^{3}+x^{2}-6 x$ on $[-1,4]$ Solution:...
Read More →An alpha particle is projected vertically upward with a speed of
Question: An alpha particle is projected vertically upward with a speed of $3.0 \times 10^{4} \mathrm{~km} / \mathrm{s}$ in a region where a magnetic field of magnitude 1.0T exists in the direction south to north. Find the magnetic force that acts on the $\alpha-$ particle. Solution:...
Read More →A plate of area 10 cm squer is to be electroplated with copper
Question: A plate of area $10 \mathrm{~cm}^{2}$ is to be electroplated with copper (density $9000 \mathrm{~kg} / \mathrm{m}^{3}$ ) to a thickness of 10 micrometers on both sides, using a cell of 12V. Calculate the energy spent by the cell in the process of deposition. If this energy is used to heat $100 \mathrm{~g}$ of water, calculate the rise in the temperature of the water. ECE of copper= $3 \times 10^{-7} \mathrm{~kg} / \mathrm{C}$ and specific heat capacity of water $=4200 \mathrm{~J} / \ma...
Read More →The potential difference across the terminals of a battery of
Question: The potential difference across the terminals of a battery of emf $12 \mathrm{~V}$ and internal resistance $2 \Omega$ drops to $10 \mathrm{~V}$ when it is connected to a silver voltameter. Find the silver deposited at the cathode in half an hour. Atomic weight of silver is $107.9$ $\mathrm{g} /$ mole. Solution:...
Read More →Figure shows an electrolyte of AgCl through which a current is passed.
Question: Figure shows an electrolyte of $\mathrm{AgCl}$ through which a current is passed. It is observed that $2.68 \mathrm{~g}$ of silver is deposited in 10 minutes on the cathode. Find the heat developed in the $20^{\Omega}$ resistor during this period. Atomic weight of silver is $107.9$ $\mathrm{g} /$ mole. Solution:...
Read More →A brass plate having surface area
Question: A brass plate having surface area $200 \mathrm{~cm}^{2}$ on one side is electroplated with $0.10 \mathrm{~mm}$ thick silver layers on both sides using a $15 \mathrm{~A}$ current. Find the time taken to do the job. The specific gravity of silver is $10.5$ and its atomic weight is $107.9 \mathrm{~g} / \mathrm{mol}$. Solution:...
Read More →Two voltameters, one having a solution of silver salt and
Question: Two voltameters, one having a solution of silver salt and the other of a trivalent-metal salt, are connected in series and a current of $2 \mathrm{~A}$ is maintained for $1.50$ hours. It is found that $1.00 \mathrm{~g}$ of the trivalent-metal is deposited. (a) What is the atomic weight of the trivalent metal? (b) How much silver is deposited during this period? Atomic weight of silver is $107.9 \mathrm{~g} / \mathrm{mole}$. Solution:...
Read More →Find the time required to liberate 1.0 liter of
Question: Find the time required to liberate $1.0$ liter of hydrogen at STP in an electrolytic cell by a current of $5.0$ A. Solution:...
Read More →Verify Lagrange's mean-value theorem for the following function:
Question: Verify Lagrange's mean-value theorem for the following function: $f(x)=2 x^{2}-3 x+1$ on $[1,3]$ Solution:...
Read More →An electroplating unit plates 3.0g of silver on a brass plate in 3.0 minutes.
Question: An electroplating unit plates $3.0 \mathrm{~g}$ of silver on a brass plate in $3.0$ minutes. Find the current used by the unit. The electrochemical equivalent of silver is $1.12 \times 10^{-6} \mathrm{~kg} / \mathrm{C}$. Solution:...
Read More →Find the amount of silver liberated at cathode if
Question: Find the amount of silver liberated at cathode if $0.500 \mathrm{~A}$ of current is passed through $\mathrm{Ag}^{\mathrm{NO}_{3}}$ electrolyte for 1 hour. Atomic weight of silver is $107.9 \mathrm{~g} / \mathrm{mole}$. Solution:...
Read More →Verify Lagrange's mean-value theorem for the following function:
Question: Verify Lagrange's mean-value theorem for the following function: $f(x)=x^{2}+x-1$ on $[0,4]$ Solution:...
Read More →Find the charge required to flow through an electrolyte
Question: Find the charge required to flow through an electrolyte to liberate one atom of (a) a monovalent material and (b) a divalent material. Solution:...
Read More →Verify Lagrange's mean-value theorem for the following function:
Question: Verify Lagrange's mean-value theorem for the following function: $f(x)=x^{2}+2 x+3$ on $[4,6]$ Solution:...
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