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6 months ago

Physics Physics Mechanical Properties of Solids

Potential energy as a function of r is given by $U = \frac{A}{r^{10}} - \frac{B}{r^{5}}$ , where r is the interatomic distance, A and B are positive constant. The equilibrium distance between the two atoms will be

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Payal Gupta

Contributor-Level 10

$\frac{d U}{d r} = 0 \Rightarrow \frac{d}{d r} [\frac{A}{r^{10}}] - \frac{d}{d r} [\frac{B}{r^{5}}]$

$\Rightarrow \frac{d}{d r} [A r^{- 10}] - \frac{d}{d r} [B r^{- 5}] = 0$

$\Rightarrow - 10 A r^{- 11} + 5 B r^{- 6} = 0$

$r = {(\frac{2 A}{B})}^{\frac{1}{5}}$

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6 months ago

Physics Class 12th

Statement – I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.

Statement – II : In ac circuit, the average power delivered by the source never becomes zero.

In the light of the above statements, choose the correct answer from the options given below

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Payal Gupta

Contributor-Level 10

Z = $\sqrt[]{R^{2} + {(x_{C} - x_{L})}^{2}},$ if only L & C are present then R = 0 then p = 0

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6 months ago

Physics Physics Moving Charges and Magnetism

A proton, a deuteron and an α - particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is

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Payal Gupta

Contributor-Level 10

$r = \frac{m v}{q B} = \frac{\sqrt[]{2 m k . E}}{q B}$

$r \propto \frac{\sqrt[]{m}}{q}$

m_p = m

q_p = q

m_d = 2m

q_d = q

m_a = 4m

q_a = 2q

$\frac{r_{p}}{r_{d}} = \frac{\sqrt[]{m_{p}} * q_{d}}{q_{P} * \sqrt[]{m_{d}}}$

$\frac{r_{d}}{r_{α}} = \sqrt[]{2}$

$r_{p} : r_{d} : r_{α} = 1 : \sqrt[]{2} : 1$

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6 months ago

Physics Class 12th

The soft-iron is a suitable material for making an electromagnet. This is because soft iron has

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Payal Gupta

Contributor-Level 10

High permeability and low retentivity

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6 months ago

Physics Class 12th

What will be the most suitable combination of three resistors A = $2 Ω$ , B = $4 Ω$ , C = $6 Ω$ so that $(\frac{22}{3}) Ω$ is equivalent resistance of combination

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Payal Gupta

Contributor-Level 10

Given

$\begin{array}{l} A = 2 Ω \\ B = 4 Ω \\ C = 6 Ω \\ R_{e q} = \frac{2 * 4}{2 + 4} + 6 \end{array}$

$R_{e q} = \frac{22}{3} Ω$

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6 months ago

Physics Physics Oscillations

Two massless springs with spring constants 2k and 9k, carry 50g and 100g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then the ratio of their respective amplitudes will

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Payal Gupta

Contributor-Level 10

$ω_{1} = \sqrt[]{\frac{k}{m}} = \sqrt[]{\frac{2 k}{0.05}}$

$\begin{array}{l} \Rightarrow A_{1} ω_{1} = A_{2} ω_{2} \\ \frac{A_{1}}{A_{2}} = \frac{ω_{2}}{ω_{1}} = \sqrt[]{\frac{9 k}{0.1}} * \sqrt[]{\frac{0.05}{2 k}} \end{array}$

$\frac{A_{1}}{A_{2}} = \frac{3}{2}$

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6 months ago

Physics Class 11th

A carnot engine takes 5000 kcal of heat from a reservoir at $727 ° C$ and gives heat to a sink at $127 ° C .$ The work done by the engine is

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Payal Gupta

Contributor-Level 10

T₁ = 727 + 273 = 1000k

T₂ = 127° + 273 = 400 k

Q₁ = 5 * 10³ k cal

$\Rightarrow \frac{600}{1000} = \frac{w}{5000}$

w = 12.6 * 10⁶ J

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6 months ago

Physics System of Particles and Rotational Motion

A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be x * 10^-2 kg. The value of x is _________.

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Vishal Baghel

Contributor-Level 10

$τ_{A} = 0$

2mg *30 = Mg *10

$\Rightarrow 2 * 0.01 g * 30 = M g * 10$

M = 6 * 10^-2kg

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6 months ago

Physics Class 12th

In a potentiometer arrangement, a cell gives a balancing point at 75 cm length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emef's of two cells respectively is 3:2, the difference in the balancing length of the potentiometer wire in above two cases will be __________ cm.

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Vishal Baghel

Contributor-Level 10

$E α l$

$\Rightarrow \frac{E_{1}}{E_{2}} = \frac{l_{1}}{l_{2}}$

$\Rightarrow \frac{3}{2} = \frac{75}{l_{2}}$

$l_{2} = \frac{75 * 2}{3}$

$l_{2} = 50 c m$

$& l_{1} = 75 c m$

$Δ l = l_{1} - l_{2} = 25 c m$

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6 months ago

Physics Laws of Motion

A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2} .$ the spring constant is _________ Nm^-1. (Use g = 10 ms^-2)

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Vishal Baghel

Contributor-Level 10

COME

$k \cdot E_{i} + P \cdot E_{i} = k \cdot E_{f} + P \cdot E_{f}$

$\Rightarrow 0 + m g (h + \frac{h}{2}) = 0 + \frac{1}{2} k {(\frac{h}{2})}^{2}$ $\Rightarrow \frac{3 h}{2} m g = \frac{1}{2} k \frac{h^{2}}{4}$

$\Rightarrow 3 m g h = \frac{k}{4} h^{2} \Rightarrow 12 \frac{m g}{h} = k \Rightarrow k = \frac{12 * 0.1 * 10}{0.1}$

k = 120Nm^-1

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