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3 months ago

Class 11th Physics Motion in Plane

If $\vec{P} * \vec{Q} = \vec{Q} * \vec{P},$ the angle between $\vec{P} a n d \vec{Q} i s θ (0 ° < θ < 360 °) .$ The value of 'θ' will be………

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Payal Gupta

Contributor-Level 10

If angle between them is 180° then

$\vec{P} * \vec{Q} = \vec{q} * \vec{P} = 0$

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3 months ago

Class 11th Physics

The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity v_e such that $v_{i} = \sqrt[]{\frac{x}{y}} * v_{e} .$ The value of x will be………

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Payal Gupta

Contributor-Level 10

Using conservation of energy :

$\frac{1}{2} m v_{i}^{2} - \frac{G m m}{R} = 0 - \frac{G m m}{11 R}$

$v_{i}^{2} = \frac{20}{11} \frac{G m}{R}$

Escape velocity is defined as $\sqrt[]{\frac{2 G M}{R}}$

$v_{i} = \sqrt[]{\frac{10}{11} v_{e}}$

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3 months ago

Class 11th Physics Waves

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be………….%.

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Payal Gupta

Contributor-Level 10

$v = \sqrt[]{\frac{T}{μ}}$

new v' = $\sqrt[]{\frac{1.04 T}{μ}}$

% change = $(\sqrt[]{1.04} - 1) * 100$

= 2%

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3 months ago

Class 11th Physics Thermodynamics

A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by 52K, its efficiency is doubled. The temperature is Kelvin of the source will be…………

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Payal Gupta

Contributor-Level 10

Efficiency in the Carnot engine is defined as :

$η = \frac{w o r k}{h e a t} = \frac{1}{4}$

$η = 1 - \frac{T_{c}}{T_{h}}, 2 η = 1 - \frac{T_{c} - 52}{T_{h}} \Rightarrow T_{h} = 208 K$

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3 months ago

Class 11th Physics

Two particles having masses 4g and 16g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n : 2. The value of n will be……….

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Payal Gupta

Contributor-Level 10

$P = \sqrt[]{2 K m}$

$\frac{n}{2} = \sqrt[]{\frac{m_{1}}{m_{2}}} = \frac{1}{2}$

n = 1

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3 months ago

Class 11th Physics Oscillations

Two identical springs of spring constant '2k' are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is

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Payal Gupta

Contributor-Level 10

Since both spring applied force in same direction.

Equivalent spring constant = 4k

$T = 2 π \sqrt[]{\frac{m}{4 k}}$

$T = π \sqrt[]{\frac{m}{k}}$

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3 months ago

Class 11th Physics

Y = A sin $(ω t + ?_{0})$ is the time-displacement equation of a SHM. At t = 0 the displacement of the particle is y = $\frac{A}{2}$ and it moving along negative x-direction. Then the initial phase angle $?_{0}$ will be

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Payal Gupta

Contributor-Level 10

Using general equation of SHM :

$y = A s i n (ω t + ?_{0}) = \frac{A}{2}$

$ω t + ?_{0} = \frac{π}{6}, \frac{5 π}{6}$

At t = 0

$?_{0} = \frac{π}{6}, \frac{5 π}{6}$

Since it is moving in – x direction

$? = \frac{5 π}{6}$

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3 months ago

Class 11th Work, Energy and Power

A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v₀. It encounters and inclined plane at angle θ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel?

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Payal Gupta

Contributor-Level 10

Using conservation of energy between initial and final position shown :

$[\frac{1}{2} (\frac{2}{5} m a^{2}) {(\frac{V_{0}}{a})}^{2} + \frac{1}{2} m V_{0}^{2}] + 0 = m g l s i n θ$

$\Rightarrow \frac{7}{10} m V_{0}^{2} = m g l s i n θ$

$\Rightarrow l = \frac{7 v_{0}^{2}}{10 g s i n θ}$

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3 months ago

Class 11th Physics

Given below are two statements:

Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.

Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.

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

Translational kinetic energy will be equal to rotational kinetic energy corresponds to each degree of freedom.

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3 months ago

Class 11th Physics Motion in Straight Line

A stone is dropped from the top of a building. When it crosses a point 5m below the top, another stone starts to fall from a point 25m below the top. Both stones reach the bottom of building simultaneously. The height of the building is

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Payal Gupta

Contributor-Level 10

When second stone is released

Equation for first ball:

$x + 20 = 10 t + \frac{1}{2} g t^{2}$

Equation for second ball :

$x = \frac{1}{2} g t^{2}$

Using these two equation

20 = 10t t = 2 sec

$x = \frac{1}{2} * 10 * 4 = 20 m$

H = 20 + 20 + 5 = 45 m.

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