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3 months ago

Class 11th Physics Mechanical Properties of Solids

The normal density of a material its $ρ$ and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be

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Payal Gupta

Contributor-Level 10

From defined of bulk modulus

$K = - \frac{P}{(d V / V)} . . . . . . . (1)$

m = $ρ v = c o n s t a n t$

$ρ d V + V d ρ = 0$

$\frac{d V}{V} = - \frac{d ρ}{ρ} . . . . . . . . . (2)$

With the help of equations (1) and (2), we can write

$K = - \frac{P}{(- \frac{d ρ}{ρ})} = \frac{ρ P}{d ρ} \Rightarrow d ρ = \frac{ρ P}{K}$

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Class 11th Physics

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

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Vishal Baghel

Contributor-Level 10

Frequency increases on filing. So, initial frequency of A is 335 Hz.

f = 340 – 5 = 335 Hz

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3 months ago

Class 11th Physics

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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Vishal Baghel

Contributor-Level 10

Stress = Y * strain

=> $\frac{T_{1}}{A} = Y * - \frac{(l_{1} - l)}{l} (i)$

$\frac{T_{2}}{A} = Y * \frac{(l_{2} - l)}{l} (i i)$

=> $\frac{T_{1}}{T_{2}} = \frac{l_{1} - l}{l_{2} - l}$

$\Rightarrow l = \frac{T_{1} l_{2} - T_{2} l_{2}}{T_{1} - T_{2}} = \frac{T_{2} l_{1} - T_{1} l_{2}}{T_{2} - T_{1}}$

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Class 11th Relations and Functions

The function f(x) $= \frac{4 x^{3} - 3 x^{2}}{6} - 2 s i n x + (2 x - 1) c o s x :$

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alok kumar singh

Contributor-Level 10

$f (x) = \frac{4 x^{3} - 3 x^{2}}{6} - 2 s i n x + (2 x - 1) c o s x$

$f' (x) = 2 x^{2} - x - 2 c o s x + 2 c o s x - (2 x - 1) s i n x$

= $(2 x - 1) (x - s i n x) \geq 0 f o r x \geq 0$

$f' (x) \geq 0 \forall x \geq 1 / 2$

$∴ f (x)$ is increasing in $[\frac{1}{2}, \infty)$

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Class 11th Physics Motion in Plane

A planet revolving in elliptical orbit has:

(A) a constant velocity of revolution.

(B) has the least velocity when it is nearest to the sun.

(C) its areal velocity is directly proportional to its velocity.

(D) areal velocity in inversely proportional to its velocity.

(E) To follow a trajectory such that the areal velocity is constant.

Choose the correct answer from the options given below

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Payal Gupta

Contributor-Level 10

In elliptical orbit, areal velocity is constant

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Class 11th Maths

The locus of the mid- point of the line segment joining the focus of the parabola y² = 4ax to a moving point of the parabola, is another parabola whose directrix is:

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alok kumar singh

Contributor-Level 10

$h = \frac{a (1 + t^{2})}{2} . . . . . . . (i)$

k = at ……… (ii)

From (i) & (ii) $\frac{2 h}{a} = 1 + \frac{k^{2}}{a^{2}}$

$∴$ required locus of Q is y² = 2a (x – a/2)

Equation of directrix x – a/2 = -a/2-> x = 0

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Class 11th Physics

The trajectory of a projectile in an vertical plane is y = αx - βx², where α and β are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection θ and the maximum height attained H are respectively given by:

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Vishal Baghel

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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Class 11th Maths

A scientific committee is to be formed form 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways the committee and be formed is:

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alok kumar singh

Contributor-Level 10

I (6) F (8)

Case I 2 4

Case II 3 6

Case III 4 8

Total =

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Class 11th 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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Vishal Baghel

Contributor-Level 10

mg – T = ma. (1)

T * R = l . (2)

a = 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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Class 11th Maths

If one of the diameters of the circle x² + y² – 2x – 6y + 6 = 0 is a chord of another circle 'C', whose centre is at (2, 1), then its radius is_________

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alok kumar singh

Contributor-Level 10

$x^{2} + y^{2} - 2 x - 6 y + 6 = 0$ centre (1, 3)

$\begin{array}{l} r = \sqrt[]{1 + 9 - 6} = 2 \\ C M = \sqrt[]{1 + 4} = \sqrt[]{5} \end{array}$

$r = \sqrt[]{5 + 4} = 3$

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