Class 12th

In a meter bridge experiment, the galvanometer shows a null point when jockey is pressed at 40.0cmusing a standard resistance of 100 $Ω$ as per the diagram. The least count of the scale used is 1 mm. The unknown resistance is nearly

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Contributor-Level 10

$\Rightarrow \frac{R}{100} = \frac{40}{60}$

$\Rightarrow Δ R = (\frac{Δ l}{l} + \frac{Δ l}{(100 - l)}) R$

$= (\frac{0.1}{40} + \frac{0.1}{60}) * 66.7 = 0.27 = 0.3$

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A uniform wire of resistance $R$ is stretched uniformly to $n$ times. It is then cut to form five wires of equal length. These wires are arranged as shown in figure. the effective resistance between $A$ and $C$ is

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Contributor-Level 10

When wire is stretched uniformly

$R \propto R$

$\frac{R}{R^{'}} = {(\frac{l}{n l})}^{2} = \frac{1}{n^{2}}$

$R^{'} = n^{2} R$

When this elongated wire is cut into 5 parts, resistance of each part $= \frac{n^{2} R}{5}$

Effective resistance between A and C $= \frac{n^{2} R}{5}$

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An electric bulb and a capacitor are connected in series with an AC source. On increasing the frequency of the source, the brightness of the bulb:

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Contributor-Level 10

$X_{C} = \frac{1}{ω C}$

On increasing $ω$ XC decreases so Z decreases, current in circuit increases.

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A direct current of 4 A and an alternating current of 4 A flows through two identical resistors. The ratio of heat produced in the two resistances in same time interval will be

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Class 12th Physics Electromagnetic Waves

Contributor-Level 10

$\frac{H_{D . C .}}{H_{A . C .}} = \frac{I^{2} R}{I_{r m s}^{2} R} = 1$

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An electromagnetic wave propagates in a medium, whose electric field vector is given as E = 200sin (18 * 10⁸t + 8x) V m^-¹. Retractive index of medium and amplitude of magnetic field will be

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Class 12th Physics Electromagnetic Waves

Contributor-Level 10

$B_{0} = \frac{E_{0}}{v} v = \frac{ω}{k}$

$\Rightarrow μ = \frac{c}{v} = \frac{3 * 1 0^{8}}{\frac{9}{4} * 1 0^{8}} = \frac{4}{3}$

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ISRO observed the wavelength of sodium line emitted by a star is 589.6 nm. The actual wavelength emitted by star is 589 nm. The speed of the star with respect to us would be

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Class 12th Electromagnetic Induction

Contributor-Level 10

$\frac{Δ λ}{λ} = \frac{v}{c}$

$\Rightarrow v = \frac{0.6 * 1 0^{- 9} * 3 * 1 0^{8}}{589 * 1 0^{- 9}}$ = 3.06 * 10⁵ m/s

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Magnetic flux through a closed conducting loop of resistance $4 Ω$ changes with time as $? = (2 t^{2} + 8 t + 6)$ Wb, where t is time in seconds. The heat produced from t = 0 to t = 2 s is

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Class 12th Chemistry Solutions

Contributor-Level 10

^{$e = | \frac{d ?}{d t} | = 4 t + 8$}

^{$\Rightarrow i = \frac{e}{R} = \frac{4 t + 8}{4} = t + 2$}

^{$\Rightarrow$
Heat produced (H)=
$\int_{0}^{2} i^{2} R d t$}

^{$\Rightarrow H = 4 ⌊ \frac{8}{3} + 8 + 8 ⌋ = \frac{224}{3} J$}

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A block of mass $2 m$ is moving with speed $v$ towards a spring block system as shown in the figure. if collision of the two blocks is perfectly inelastic then maximum compression in the spring will be

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Contributor-Level 10

Applying conservation of momentum for collision of blocks

$2 m v + 0 = 3 m v^{'}$

$? v^{'} = \frac{2 v}{3} \dots (1)$

Now, from conservation of energy

$\frac{1}{2} * 3 m * {v^{'}}^{2} = \frac{1}{2} k x_{0}^{2}$

$x_{0} = \sqrt[]{\frac{3 m v^{' 2}}{k}} = v' \sqrt[]{\frac{3 m}{k}}$

$= \frac{2 v}{3} \sqrt[]{\frac{3 m}{k}} = v \sqrt[]{\frac{4 m}{3 k}}$

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Class 12th Chemistry

From a sprinkler of length $1 m$ , water is throw out with $0.5 m / s$ tangentially at the rate of $0.6 k g / m i n$ . If diameter of sprinkler is $8 c m$ and moment of inertia is $500 g c m^{2}$ , the rate at which angular speed of sprinkler will increases is (assume there in no resistance to motion)

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Contributor-Level 10

Angular momentum imparted to sprinkler per

$s e c o n d = v r \frac{d m}{d t} = \frac{0.6}{60} * 0.5 * 1 = 0.005 N . m$

$? l \frac{d ω}{d t} = 0.005$

$? \frac{d ω}{d t} = \frac{0.005}{500 * 10^{- 7}}$

$= 100 \frac{r a d}{s^{2}}$

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Class 12th Chemistry

A prism has refracting angle of 30⁰ and it is made of glass of refractive index $\sqrt[]{2}$ . At what angle should a light ray be incident on a face of prism such that it passes normally through the other face?

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