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Physics Nuclei

A radioactive simple is undergoing decay. At any time t₁, its activity is A and another time t₂, the activity is $\frac{A}{5} .$ What is the average life time for the sample?

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Payal Gupta

Contributor-Level 10

$A = A_{0} e^{- λ t_{1}}$ [Radio active decay law]

$\frac{A}{5} = A_{0} e^{- λ (t_{2} - t_{1})}$

$\Rightarrow l n 5 = λ (t_{2} - t_{1})$

$\Rightarrow A v e r a g e l i f e = \frac{1}{λ} = \frac{(t_{2} - t_{1})}{l n 5}$

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Physics Mechanical Properties of Solids

The length of metallic wire is $l_{1}$ when tension in it is $T_{1}$ . It is $l_{2}$ when the tension is T₂. The original length of the wire will be

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a year ago

Physics Motion in a Plane

The trajectory of a projectile in an vertical plane is y = ax - bx², where a and b are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection q and the maximum height attained H are respectively given by

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Payal Gupta

Contributor-Level 10

$y = α x - β x^{2}$

$\Rightarrow \frac{d y}{d x} = α - 2 β x = 0$

$\Rightarrow x = \frac{α}{2 β}$

$y_{m a x} = α * \frac{α}{2 β} - β * {(\frac{α}{2 β})}^{2} = \frac{α^{2}}{4 β}$

Range = $2 x = \frac{α}{β} = \frac{2 u^{2} s i n θ . c o s θ}{g}$

On comparing with

y = x tan θ- $\frac{g x^{2}}{2 u^{2} c o s^{2} θ}$

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Physics System of Particles and Rotational Motion

A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertial about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance 'h', the square of angular velocity of wheel will be

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Payal Gupta

Contributor-Level 10

mg – T = ma. (1)

T * R = l α. (2)

a = α R. (3)

With the help of equations (1), (2) and (3), we get

$a = \frac{m g}{m + \frac{l}{R^{2}}}$

$v = \sqrt[]{2 a h} = ω R$

$\Rightarrow ω^{2} = \frac{2 m g h}{l + m R^{2}}$

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Physics physics ncert exemplar solution class 12th chapter one

Two charged thin infinite plane sheets of uniform surface charge density $σ_{+}$ and $σ_{-}$ , where $|σ_{+}| > |σ_{-}|$ , intersect at right angle. Which of the following best represents the electric field lines for this system.

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alok kumar singh

Contributor-Level 10

$\Rightarrow$ Electric field due to infinite sheet is uniform.

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Physics Physics NCERT Exemplar Solutions Class 12th Chapter Six

A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil?

Three positions shown describe:

(a) The magnet's entry

(b) Magnet is completely inside and

(c) Magnet's exit

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alok kumar singh

Contributor-Level 10

Kindly go through the solution

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Physics Moving Charges and Magnetism

An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface. Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

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Payal Gupta

Contributor-Level 10

Using Ampere's law for long hollow cylinder carrying current on its surface

B_in = 0

$B_{o u t} = \frac{μ_{0} i}{2 π r}$

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Physics Physics NCERT Exemplar Solutions Class 12th Chapter Twelve

Match the $C_{p} / C_{V}$ ratio for ideal gases with different type of molecules:

Match the correct option?

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alok kumar singh

Contributor-Level 10

Mono atomic $? C_{v} = \frac{3 R}{2} C_{p} = \frac{5 R}{2}$

Di- atomic $? C_{V} = \frac{5 R}{2} C_{p} = \frac{7 R}{2}$

(Rigid)

Di-atomic $? C_{v} = \frac{7 R}{2} C_{p} = \frac{9 R}{2}$

(Non-Rigid)

Tri-atomic $? C_{V} = 3 R C_{P} = 4 R$

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Physics physics ncert exemplar solutions class 12th chapter two

A two point charges $4 q$ and $- q$ are fixed on the $x$ -axis at $x = - \frac{d}{2}$ and $x = \frac{d}{2}$ , respectively. If a third point charge ' $q$ ' is taken from the origin to $x = d$ along the semicircle as shown in the figure, the energy of the charge will:

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alok kumar singh

Contributor-Level 10

$U_{initial} = \frac{k (4 q) (q)}{(d / 2)} + \frac{k (q) (- q)}{(d / 2)}$

$\begin{array}{r} \Rightarrow \frac{6 k q^{2}}{d} \\ \Rightarrow U_{final} = \frac{4 (4 q) (q)}{(\frac{3 d}{2})} + \frac{k (q) (- q)}{(d / 2)} \\ \Rightarrow \frac{2}{3} \frac{k q^{2}}{d} \\ \Rightarrow Δ U = (\frac{2}{3} - 6) \frac{k q^{2}}{d} \Rightarrow \frac{- 16}{3} \frac{{k q}^{2}}{d} \end{array}$

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Physics Physics NCERT Exemplar Solutions Class 12th Chapter Fourteen

Take the breakdown voltage of the zener diode used in the given circuit as $6 V$ . For the input voltage shown in figure below, the time variation of the output voltage is: (Graphs drawn are schematic and not to scale)

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alok kumar singh

Contributor-Level 10

Kindly go through the solution

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