Physics

The volume charge density of a sphere of radius 6m is 2 $μ C c m^{- 3} .$ The number of lines of force per unit surface area coming out from the surface of the sphere is _________ * 10¹⁰ NC^-1.

[Given : Permittivity of vacuum $\in_{0} = 8.85 * 1 0^{- 12} C^{2} N^{- 1} - m^{- 2}]$

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Contributor-Level 10

No. of electric field line per unit area = electric field

$E = \frac{ρ r}{3 \in_{0}} f o r r = R$

$E = 45 * 1 0^{10} N / C$

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5 months ago

An observer is riding on a bicycle and moving towards a hill at 18 kmh^-1. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and velocity of the sound in air is 320 m/s, the beat frequency between the two sounds heard by observer will be _________ Hz.

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Contributor-Level 10

$v_{S} = 0, v_{O_{b}} = 5 m / s$

$f_{d i r e c t} = (\frac{320 - 5}{320}) 640 = 630 H z$

$f_{b e a t} = (650 - 630) = 20 H z$

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5 months ago

A unit scale is to be prepared whose length dows not change with temperature and remains 20cm, using a bimetallic strip made of bass and iron each of different length. The length of both components would change in such a way that difference between their length remains constant. If length of brass is 40cm and length of iron will be ________cm.

$(α_{i r o n} = 1.2 * 1 0^{- 5} K^{- 1} a n d α_{b r a s s} = 1.8 * 1 0^{- 5} K^{- 1}) .$

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Physics Mechanical Properties of Fluids

Contributor-Level 10

$l_{B} (1 + α_{B} Δ T) - l i (1 + α_{i} Δ T) = l_{B} - l_{i}$

$\Rightarrow α_{B} l_{B} = l_{i} α_{i}$

$l_{i} = 60 c m$

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5 months ago

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5cm. Another wire of the same material of length 4L and radius 4r pulled by a force 4F under same conditions. The increases in length of this wire is _________cm.

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Contributor-Level 10

$Δ L_{1} = \frac{F L}{A Y} = \frac{F L}{π r^{2} Y} = 5 c m$

$Δ L_{2} = \frac{4 F 4 L}{π 16 r^{2} y}$ = $\frac{F L}{π r^{2} Y} = 5 c m$

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5 months ago

Four forces are acting at a point P in equilibrium as shown in figure. The ratio of force F₁ to F₂ is 1: x where x = _________.

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Contributor-Level 10

$F_{2} = 1 c o s 45 ° + 2 c o s 45 ° = 3 c o s 45 ° = \frac{3}{\sqrt[]{2}} N$

$\begin{array}{l} F_{1} + 1 c o s 45 ° = 2 s i n 45 ° \\ \frac{F_{1}}{F_{2}} = 1 : 3 \end{array}$

x = 3

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5 months ago

A car is moving with speed of 150 km/h and after applying the break it will move 27m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling _________m distance.

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Contributor-Level 10

Stopping distance = $\frac{v^{2}}{2 a} = d$ $\frac{^{}}{}$

If speed is made $\frac{1}{3} r d$ $\frac{}{}$

$d^{1} = \frac{d}{9}, d^{1} = \frac{27}{9} = 3 m$

Braking acceleration Remains same.

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6 months ago

A capacitor of capacitance 500 $μ F$ is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. Then maximum current in LC circuit will be_______ A.

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Contributor-Level 10

C = 500 $μ F,$ V = 100 v, L = 50 mH

In this LC – oscillation

q = q₀ cos $ω t$

$i = \frac{- d q}{d t} = q_{0} ω s i n ω t ω = \frac{1}{\sqrt[]{2 c}} = \frac{1}{\sqrt[]{50 * 1 0^{- 3} * 5 * 1 0^{- 4}}}$

= $\frac{1000}{5} = 200$

So, i_max = $q_{0} ω = 500 * 1 0^{6} * 100 * 200$

= 10A

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6 months ago

Physics Physics Nuclei

Two radioactive materials A and B have decay constants 25 $λ$ and 16 $λ$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be “e” after a time $\frac{1}{a λ} .$ The value of a is__________.

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Contributor-Level 10

$λ_{A} = 25 λ,$ $λ_{B} = 16 λ$

At t = 0 N_A = N_B = N₀

after t = $\frac{1}{a λ} : - \frac{N_{B}}{N_{A}} = \frac{N_{0} e^{- 16 λ t}}{N_{0} e^{- 25 λ t}} = e^{(25 λ - 16 λ) t}$

e = $e^{(9 λ \frac{1}{a λ})}$

$\Rightarrow \frac{9}{a} = 1 \Rightarrow a = 9$

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6 months ago

A 8 V Zener diode along with a series resistance R is connected across a 20V supply (as shown in the figure). If the maximum Zener current is 25 mA, then the minimum value of R will be_______ $Ω$ .

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Contributor-Level 10

$i_{(z e n e r - m a x)} = 25 m A$

20 – i_max R – 8 = 0

i_max R = 12

At minimum zener current $(μ A) : -$

$20 - i_{m i n} R - i_{m i n} R_{L} = 0$

$\frac{R}{R_{L}} = \frac{12}{8} = \frac{3}{2}$

$l_{m i n} R = 12$

$i_{m i n} R_{L} = 8$

At maxm zener current –

$20 - i_{m a x} R - 8 = 0$

$i_{L} = O {a s i_{z} m a x^{m} = 25 m A}$

i_maxR = 12v

25 * 103 R = 12

$R = \frac{12 * 1 0^{3}}{25} = 12 * 40 = 480 Ω$

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6 months ago

The metallic bob of simple pendulum has the relative density. 5 The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes $5 \sqrt[]{x} s .$ The value of x will be_______.

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