Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\sin x}{\sin (x-\alpha)} d x=?$ A. $x \cos \alpha+(\sin \alpha) \log |\sin (x-\alpha)|+C$ B. $x \sin \alpha+(\sin \alpha) \log |\sin (x-\alpha)|+C$ C. $x \cos \alpha-(\sin \alpha) \log |\sin (x-\alpha)|+C$ D. $x \sin \alpha-(\sin \alpha) \log |\sin (x-\alpha)|+C$ Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{\left(\sin ^{3} x+\cos ^{3} x\right)}{\sin ^{2} x \cos ^{2} x} d x=?$ A. $\sin x-\cos x+C$ B. $\tan x-\cos x+C$ C. $\sec x-\operatorname{cosec} x+C$ D. None of these Solution:...
Read More →Find the speed at which the kinetic energy of a particle will differ by
Question: Find the speed at which the kinetic energy of a particle will differ by $1 \%$ from its nonrelativistic value ${ }^{\frac{1}{2}} \mathrm{~m}_{0} \mathrm{v}^{2}$. Solution:...
Read More →What is the kinetic energy of an electron in electron volts
Question: What is the kinetic energy of an electron in electron volts with mass equal to double its rest mass? Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \frac{(a x+b)}{(c x+d)} d x=?$ A. $\frac{\mathrm{ax}}{\mathrm{c}}+\log |\mathrm{cx}+\mathrm{d}|+\mathrm{C}$ B. $\frac{a}{c}+\log |c x+d|+C$ C. $\frac{a x}{c}+\frac{(b c-a d)}{c^{2}} \log |c x+d|+C$ D. None of these Solution:...
Read More →Find the speed of an electron with kinetic energy
Question: Find the speed of an electron with kinetic energy (a) $1 \mathrm{eV}$, (b) $10 \mathrm{keV}$ and (c) $10 \mathrm{MeV}$. Solution:...
Read More →Through what potential difference should an electron
Question: Through what potential difference should an electron be accelerated to give it a speed of (a) $0.6 \mathrm{c}$, (b) $0.9 \mathrm{c}$ and (c) $0.99 \mathrm{c}$ ? Solution:...
Read More →Find the mass, kinetic energy and the momentum of
Question: Find the mass, kinetic energy and the momentum of an electron moving at $0.8 \mathrm{c}$. Solution:...
Read More →An electron and a positron moving at small speeds collide and annihilate each other.
Question: An electron and a positron moving at small speeds collide and annihilate each other. Find the energy of the resulting gamma photon. Solution:...
Read More →The energy from the sun reaches just outside the earth's atmosphere
Question: The energy from the sun reaches just outside the earth's atmosphere at a rate of $1400 \mathrm{w} / \mathrm{m}^{2}$. The distance between the sun and the earth is $1.5 \times 10^{11} \mathrm{~m}$. (a) Calculate the rate at which the sun is losing its mass. (b) How long will the sun last assuming a constant decay at this rate? The present mass of the sun is $2 \times 10^{30} \mathrm{~kg}$. Solution:...
Read More →A 100W bulb together with its power supply is suspended from
Question: A $100 \mathrm{~W}$ bulb together with its power supply is suspended from a sensitive balance. Find the change in the mass recorded after the bulb remains on for 1year. Solution:...
Read More →By what fraction does the mass of a boy increase
Question: By what fraction does the mass of a boy increase when he starts running at a speed of $12 \mathrm{~km} / \mathrm{h}$ ? Solution:...
Read More →Find the loss in the mass of 1 mole of an ideal monatomic gas kept in a rigid
Question: Find the loss in the mass of 1 mole of an ideal monatomic gas kept in a rigid container as it cools down by $10^{\circ} \mathrm{C}$. The gas constant $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$. Solution:...
Read More →Find the increase in mass when 1kg of water is heated from 0°c to 1000c.
Question: Find the increase in mass when $1 \mathrm{~kg}$ of water is heated from $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$. Specific heat capacity of water=4200 $\mathrm{J} / \mathrm{kg}-\mathrm{K}$. Solution:...
Read More →By what fraction does the mass of a spring change
Question: By what fraction does the mass of a spring change when it is compressed by $1 \mathrm{~cm}$ ? The mass of the spring is $200 \mathrm{~g}$ at its natural length and the spring constant is $500 \mathrm{~N} / \mathrm{m}$. Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int\left(\frac{\left(x^{4}+1\right)}{\left(x^{2}+1\right)}\right) d x=?$ A. $\frac{x^{3}}{3}+x-\tan ^{-1} x+C$ B. $\frac{x^{3}}{3}-x-2 \tan ^{-1} x+C$ C. $\frac{x^{3}}{3}+x-2 \tan ^{-1} x+C$ D. None of these Solution:...
Read More →A particular particle created in a nuclear reactor leaves a
Question: A particular particle created in a nuclear reactor leaves a $1 \mathrm{~cm}$ track before decaying. Assuming that the particle moved at $0.995 \mathrm{c}$, calculate the life of the particle (a) in the lab frame and (b) in the frame of the particle. Solution:...
Read More →At what speed the volume of an object shrinks to half its rest value?
Question: At what speed the volume of an object shrinks to half its rest value? Solution:...
Read More →A person travelling by a car moving at a speed of
Question: A person travelling by a car moving at a speed of $100 \mathrm{~km} / \mathrm{h}$ finds that his wristwatch agrees with the clock on a tower A. By what amount will his wristwatch lag or lead the clock on another tower B, $1000 \mathrm{~km}$ (in the earth's frame) from the tower A when the car reaches there? Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \tan ^{-1}(\operatorname{cosec} x-\cot x) d x=?$ A. $\frac{x^{2}}{4}+C$ B. $\frac{-\mathrm{X}^{2}}{4}+C$ C. $\frac{x^{2}}{2}+C$ D. $\frac{-x^{2}}{2}+C$ Solution:...
Read More →An electric bulb, connected to a make and break power supply,
Question: An electric bulb, connected to a make and break power supply, switches off and on every second in its rest frame. What is the frequency of its switching off and on as seen from a spaceship travelling at a speed of $0.8 c$ ? Solution:...
Read More →If a person lives on the average 100 years in his rest frame,
Question: If a person lives on the average 100 years in his rest frame, how long does he live in the earth frame if he spends all his life on a spaceship going at $60 \%$ of the speed of light? Solution:...
Read More →Suppose swarglok (heaven) is in constant motion at a speed of
Question: Suppose swarglok (heaven) is in constant motion at a speed of $0.9999 \mathrm{c}$ with respect to the earth. According to the earth's frame, how much time passes on the earth before one day passes on swarglok? Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \cos ^{-1}\left(\frac{1-\tan ^{2} x}{1+\tan ^{2} x}\right) d x=?$ A. $x^{2}+C$ B. $-\mathrm{x}^{2}+\mathrm{C}$ C. $\frac{1}{\sqrt{1+x^{2}}}+C$ D. $\frac{1}{\sqrt{1-x^{2}}}+C$ Solution:...
Read More →Two babies are born in a moving train,
Question: Two babies are born in a moving train, one in the compartment adjacent to the engine and the other in the compartment adjacent to the guard. According, to the train frame, the babies are born at the same instant of time. Who is elder according to the ground frame? Solution: As frame is in motion $\therefore$ clocks are out of sync. So, if $L^{\prime}$ is length of train in rest and speed of train is $v$ in moving frame then the clock at one end where guard is standing leads the one nea...
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