Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=(\log x)^{x}$ Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: $y=x^{\sqrt{x}}$ Solution:...
Read More →Solve this following
Question: Find $\frac{d y}{d x}$, when: []$_{y}=x^{1 / x}$ Solution: Here, we need to take log both the sides to get that differentiation simple....
Read More →A particle of mass 1 g and charge
Question: A particle of mass $1 \mathrm{~g}$ and charge $2.5^{\times 10^{-4}} \mathrm{C}$ is released from rest in an electric field of $1.2^{\times 10^{-4}} \mathrm{~N} / \mathrm{C}$. (a) Find the electric force and the force of gravity acting on this particle. Can one of these forces be neglected in comparison with the other for approximate analysis? (b) How long will it take for the particle to travel a distance of $40 \mathrm{~cm}$ ? (c) What will be the speed of the particle after travellin...
Read More →Solve this following
Question: Find , when: If $\cos ^{-1}\left(\frac{x^{2}-y^{2}}{x^{2}+y^{2}}\right)=\tan ^{-1} a$, prove that $\frac{d y}{d x}=\frac{y}{x}$ Solution:...
Read More →A particle of mass m and charge q
Question: A particle of mass $m$ and charge $q$ is thrown at a speed against a uniform electric field $\mathrm{E}$. How much distance will it travel before coming to momentary rest? Solution:...
Read More →Solve this following
Question: Find, when: If $\cos y=x \cos (y+a)$, prove that $\frac{d y}{d x}=\frac{\cos ^{2}(y+a)}{\sin a}$. Solution:...
Read More →Solve this following
Question: Find, when: If $y \log x=(x-y)$, prove that $\frac{d y}{d x}=\frac{\log x}{(1+\log x)^{2}}$ Solution:...
Read More →Solve this following
Question: Find, when: If $x y=\tan (x y)$, show that $\frac{d y}{d x}=\frac{-y}{x}$ Solution:...
Read More →Solve this following
Question: Find, when: If $y=x \sin y$, prove that $\left(x \cdot \frac{d y}{d x}\right)=\frac{y}{(1-x \cos y)}$ There is correction in question .... Prove that should be $\frac{d y}{d x}=\frac{\sin y}{1-x \cos y}$ instead of $\left(\mathrm{x} \cdot \frac{\mathrm{dy}}{\mathrm{dx}}\right)=\frac{\mathrm{y}}{(1-\mathrm{x} \cos \mathrm{y})}$ to get the required answer. Solution:...
Read More →Solve this following
Question: Find, when: $\log \sqrt{x^{2}+y^{2}}=\tan ^{-1} \frac{y}{x}$ Solution:...
Read More →Solve this following
Question: Find, when: $e^{x} \log y=\sin ^{-1} x+\sin ^{-1} y$ Solution:...
Read More →A pendulum bob of mass 80mg and carrying a charge of
Question: A pendulum bob of mass $80 \mathrm{mg}$ and carrying a charge of $2^{\times 10^{-8}} \mathrm{C}$ is at rest in a uniform, horizontal electric field of $20 \mathrm{kV} / \mathrm{m}$. Find the tension in the thread. Solution:...
Read More →A positive charge q is placed in front of a conducting solid cube
Question: A positive charge $q$ is placed in front of a conducting solid cube at a distance $d$ from its centre. Find the electric field at the centre of the cube due to the charges appearing on its surface. Solution:...
Read More →A circular wire-loop of radius a carries a total charge Q
Question: A circular wire-loop of radius a carries a total charge $Q$ distributed uniformly over its length. A small length dL of the wire is cut off. Find the electric field at the centre due to the remaining wire. Solution:...
Read More →A wire is bent in the form of a regular hexagon and
Question: A wire is bent in the form of a regular hexagon and a total charge $q$ is distributed uniformly on it. What is the electric field at the centre? You may answer this part without making any numerical calculations. Solution: Regular hexagon is an equipotentential surface Thus charge at every point on surface is same. Therefore, Net electric field at centre is zero....
Read More →Consider a uniformly charged ring of radius R.
Question: Consider a uniformly charged ring of radius $R$. Find the point on the axis where the electric field is maximum. Solution:...
Read More →A 10 cm long rod carriers a charges of +50 μc distributed uniformly along its length.
Question: A $10 \mathrm{~cm}$ long rod carriers a charges of $+50 \mu \mathrm{c}$ distributed uniformly along its length. Find the magnitude of the electric field at a point $10 \mathrm{~cm}$ from both the ends of the rods. Solution:...
Read More →