Estimate the number of electrons in
Question: Estimate the number of electrons in $100 \mathrm{~g}$ of water. How much is the total negative charge on these electrons? Solution:...
Read More →Two charged particles are placed at a distance
Question: Two charged particles are placed at a distance $1.0 \mathrm{~cm}$ apart. What is the minimum possible magnitude of the electric force acting on each charge? Solution:...
Read More →Suppose the second charges in the previous problem
Question: Suppose the second charges in the previous problem are $-1.0 \times 10^{-6} \mathrm{C}$. Locate the position where a third charge will not experience a net force. Solution:...
Read More →Prove the following
Question: Two charges $2.0 \times 10^{-6} \mathrm{C}$ and $1.0^{\times 10^{-6}} \mathrm{C}$ are placed at a separation of $10 \mathrm{~cm}$. Where a third charge should be placed such that it experiences no net force due to these charges? Solution:...
Read More →Solve this following
Question: Find, when: []$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ Solution:...
Read More →Find the electric force between two protons separated by
Question: Find the electric force between two protons separated by a distance of 1 Fermi ( 1 Fermi $\left.=10^{-15}\right)$. The protons in a nucleus remain at a separation of this order. Solution:...
Read More →Two equal charges are placed at a separation of 1.0 m.
Question: Two equal charges are placed at a separation of $1.0 \mathrm{~m}$. What should be the magnitude of the charges so that the force between them equals the weight of $50 \mathrm{~kg}$ person? Solution:...
Read More →At what separation should two equal charges,
Question: At what separation should two equal charges, $1.0 \mathrm{C}$ each, be placed so that the force between them equals the weight of a $50 \mathrm{~kg}$ person? Solution:...
Read More →A charge of 1.0 is placed at the top of the your college building
Question: A charge of $1.0$ is placed at the top of the your college building and another equal charge at the top of your house. Take the separation between the two charges to be $2.0 \mathrm{~km}$. Find the force exerted by the charges on each other. How many times of your weight is this force? Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : Differentiate $\sin ^{-1}\left(\frac{2^{x+1}}{1+4^{x}}\right)$ w.r. t. $x$ Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : If $\mathrm{y}=\tan ^{-1}\left\{\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right\}$. Prove that $\frac{d y}{d x}=\frac{1}{2 \sqrt{1-x^{2}}}$. Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : If $y=\sin \left\{2 \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right\}$, show that $\frac{d y}{d x}=\frac{-x}{\sqrt{1-x^{2}}}$. Solution:...
Read More →Find the dimensional formula of e0.
Question: Find the dimensional formula of e0. Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : If $y=\sec ^{-1}\left(\frac{x+1}{x-1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right)$, show that $\frac{d y}{d x}=0$ Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : If $y=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)+\sec ^{-1}\left(\frac{1+x^{2}}{1-x^{2}}\right)$, show that $\frac{d y}{d x}=\frac{4}{\left(1+x^{2}\right)}$ Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : If $t=\tan ^{-1}\left(\frac{a x-b}{b x+a}\right)$, prove that $\frac{d y}{d x}=\frac{1}{\left(1+x^{2}\right)}$ Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : $\tan ^{-1}\left(\frac{2 x}{1+15 x^{2}}\right)$ Solution:...
Read More →A hot body placed in a surrounding of temperature
Question: A hot body placed in a surrounding of temperature $\theta_{0}$ obeys Newton's law of cooling $\frac{d \theta}{d t}=k\left(\theta-\theta_{0}\right)$. Its temperature at $t=0$ is $\theta_{1}$. The specific heat capacity of the body is $s$ and its mass is $m$. Find (a) The maximum heat that the body can lose and (b) the time starting from $t=0$ in which it will lose $90 \%$ of this maximum heat. Solution:...
Read More →A metal block of heat capacity 80 J/°C placed in a room at 20°C
Question: A metal block of heat capacity $80 \mathrm{~J} /{ }^{\circ} \mathrm{C}$ placed in a room at $20^{\circ} \mathrm{C}$ is heated electrically. The heater is switched off when the temperature reaches $30^{\circ} \mathrm{C}$. The temperature of the block rises at the rate of $2^{\circ} \mathrm{C} / \mathrm{s}$ just after the heater is switched on and falls at the rate of $0.2^{\circ} \mathrm{C} / \mathrm{s}$ just after the heater is switched off. Assume Newton's law of cooling to hold. (a) ...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : $\tan ^{-1}\left(\frac{5 x}{1-6 x^{2}}\right)$ Solution:...
Read More →A metal ball of mass 1 kg is heated by means of a 20W
Question: A metal ball of mass $1 \mathrm{~kg}$ is heated by means of a $20 \mathrm{~W}$ heater in a room at $20^{\circ} \mathrm{C}$ The temperature of the ball becomes steady at $50^{\circ} \mathrm{C}$. (a) Find the rate of loss of heat to the surrounding when the ball is at $50^{\circ} \mathrm{C}$. (b) Assuming Newton's law of cooling, calculating the rate of loss of heat to the surrounding when the ball is at $30^{\circ} \mathrm{C}$ (c) Assume that the temperature of the ball rises uniformly ...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : $\tan ^{-1}\left(\frac{3-2 x}{1+6 x}\right)$ Solution:...
Read More →A calorimeter contains 50g of water at 50°C.
Question: A calorimeter contains $50 \mathrm{~g}$ of water at $50^{\circ} \mathrm{C}$. The temperature falls to $40^{\circ} \mathrm{C}$ in 10 minutes. When the calorimeter contains $100 \mathrm{~g}$ of water at $50^{\circ} \mathrm{C}$, it takes 18 minutes for the temperature to become $45^{\circ} \mathrm{C}$. Find the water equivalent of the calorimeter. Solution:...
Read More →Differentiate each of the following w.r.t
Question: Differentiate each of the following w.r.t $x$ : $\tan ^{-1}\left(\frac{\sqrt{a}+\sqrt{x}}{1-\sqrt{a x}}\right)$ Solution:...
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