Q: Two particles of equal mass (m) each move in a circle of radius (r) under the action of their mutual gravitational attraction the speed of the particle is

Given Masses of the two particles are \$m_{1} = m_{2} = m \$ And radius of the two particles are \$r_{1} = r_{2} = R \$ So, the Gravitational force of attraction between the particles\$F = \dfrac{G \times m \times m}{R^{2}} \$ .............. (i) And centripital force \$F = \dfrac{m \times v^{2}}{R} \$ ................(ii) From given condition (i) and (ii) \$ \dfrac{Gmm}{(2R)^{2}} = \dfrac{mv^{2}}{R} \$,\$v = \dfrac{Gm}{4R} = \dfrac{1}{2} \sqrt{\dfrac{Gm}{R}} \$ So the speed of the each particle is \$v = \dfrac{1}{2} \sqrt{\dfrac{Gm}{R}} \$

Q: Is angular momentum equal to Inertia \$\times \omega\$ and why?

\$\text{Explanation:}\$Angular momentum is also known as the moment of momentumconsider a rigid body rotating about a fixed axis with an angular velocity of \$\omega\$, whose moment of inertia is Ithe definition of I is the sum of the products of the mass and the square of the perpendicular distance to the axis of rotation of each particle in a body to the axis of rotation.i.e\$I = \sum mr^{2}\$consider the rigid body is made up of particles each of mass mthen the moment of momentum ( call it L) of each particle\$L = momentum \times r\$where r is the perp. distance from the axis\$\therefore L = mvr\$where v is the linear (tangential) velocitybut for angular motion\$v = r\omega\$so\$L = mrr\omega = mr^2\omega\$For the total angular momentum we have to sum up all the particles\$L_{T} = \sum mr^2\omega\$\$L_{T} = \omega \sum mr^2\$\$L_{T} = I\omega\$so angular momentum is moment of inertia \$\times\$ omega in vectors the formula is\$\vec{L} = \vec{r} \times m\vec{v}\$

Question 1

How many feet are in a football field that is 100 yards?

Accepted Answer

Answer300 ftExplanation :Since 1 yard = 3 feet, we can multiply 100 yd by  $\dfrac{3 ft}{1 yd} $ We are essentially multiplying by 1, but doing so allows us to cancel out the yd unit so that we are left with only ft.$ \dfrac{100 yd}{1}.\dfrac{3 ft}{1 yd} =  300 ft $

Question 2

What is the unit of viscosity? Please explain.

Accepted Answer

The viscosity of a fluid is a measure of its resistance to flow.We usually think of the viscosity of a liquid as its &#34;thickness&#34;.For example, we say that honey is &#34;thicker&#34; (has a higher viscosity) than water.One way to measure viscosity is to place the fluid between two flat parallel plates and slide one plate past the other.In terms of the above diagram, the formula for viscosity &#951; is$  \eta = \frac { F \delta }{Av } $Thus the units of visocity are $ \frac { N \times m}{ m^2 \times  m . s^{-1} }= N.sm.m^{-2} = P a.s $If a fluid is placed between two  $ 1m^2 $ plates that are 1 m apart and one plate is pushed sideways with a force of 1 N and it moves at a velocity of $ 1 m/s^{-1} $ then the fluid has a viscosity $ \eta  = 1 Pa.s $Many chemists still use an old unit of viscosity, the poise (P), named after the French physician Jean Poiseuille.It is convenient unit because $ 1m Pa.s = 1cP $For example , the viscosity of water at $ 20^0 C $ is $  1.002 mPa.s $ or $ 1.002 cP $Honey has a viscosity of about $ 10 Pa.s $ or $ 10000cP $

Question 3

Two particles of equal mass (m) each move in a circle of radius (r) under the action of their mutual gravitational attraction the speed of the particle is

Accepted Answer

Given Masses of the two particles are $m_{1} = m_{2} = m $ And radius of the two particles are $r_{1} = r_{2} = R $ So, the Gravitational force of attraction between the particles$F = \dfrac{G \times m \times m}{R^{2}} $ .............. (i) And centripital force $F = \dfrac{m \times v^{2}}{R} $ ................(ii) From given condition (i) and (ii) $ \dfrac{Gmm}{(2R)^{2}} = \dfrac{mv^{2}}{R} $,$v = \dfrac{Gm}{4R} = \dfrac{1}{2} \sqrt{\dfrac{Gm}{R}} $ So the speed of the each particle is $v = \dfrac{1}{2} \sqrt{\dfrac{Gm}{R}} $

Question 4

The dimensions of Planck's constant is

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Question 5

Is angular momentum equal to Inertia $\times \omega$ and why?

Accepted Answer

$\text{Explanation:}$Angular momentum is also known as the moment of momentumconsider a rigid body rotating about a fixed axis with an angular velocity of $\omega$, whose moment of inertia is Ithe definition of I is the sum of the products of the mass and the square of the perpendicular distance to the axis of rotation of each particle in a body to the axis of rotation.i.e$I = \sum mr^{2}$consider the rigid body is made up of particles each of mass mthen the moment of momentum ( call it L) of each particle$L = momentum \times r$where r is the perp. distance from the axis$\therefore L = mvr$where v is the linear (tangential) velocitybut for angular motion$v = r\omega$so$L = mrr\omega = mr^2\omega$For the total angular momentum we have to sum up all the particles$L_{T} = \sum mr^2\omega$$L_{T} = \omega \sum mr^2$$L_{T} = I\omega$so angular momentum is moment of inertia $\times$ omega in vectors the formula is$\vec{L} = \vec{r} \times m\vec{v}$

Question 6

Choose the correct answer from the alternatives given.Time period is the time taken to complete one oscillation. This definition of time period is true for

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Question 7

How do vectors work in physics?

Accepted Answer

Vectors are lines that represent both magnitude (size) and direction. The length of the vector is drawn to scale, to communicate the size of the measurement; the head of the arrow points in the direction in which the measurement is traveling.Vectors can be used in a number of ways. Most commonly, they are used to represent displacement or velocity of a moving object, but they can also be used to represent force.If an object moves in more than one direction subsequently, or if more than one force acts upon an object concurrently, vectors can be added to find a resultant displacement or resultant force. This can be calculated using either a scale diagram and measuring the resultant, or by use of mathematics.

Question 8

A block of mass 10 kg is placed at a distance of 5 m from the rear end of a long trolleyes shown in figure. The coefficient of friction between the block and the surface below is 0.2. Starting from the rest, the trolley is given a uniform acceleration of 3 ms. At what distance from the starting point will block fall off the trolley! Take $g = 10 ms^{-3}$

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Question 9

A uniform cylinder of mass $m = 8.0\ kg$ and radius $R = 1.3\ cm$ (Fig.) starts descending at a moment $t = 0$ due to gravity. Neglecting the mass of the thread, find:(a) the tension of each thread and the angular acceleration of the cylinder.(b) the time dependence of the instantaneous power developed by the gravitational force.

Accepted Answer

(a) Let us indicate the forces and their points of application fox the cylinder. Choosing the positive direction for $x$ and $\varphi$ as shown in the figure, we write the equation of motion of the cylinder axis and the equation of moments in the C.M. frame relative to that axis i.e. from equationi.e. from equation $F_{x} = mw_{c}$ and $N_{z} = I_{c}\beta_{x}$.$mg - 2T = mw_{c}; 2TR = \dfrac {mR^{2}}{2}\beta$As there is no slipping of thread on the cylinder$w_{c} = \beta R$From these three equations$T = \dfrac {mg}{6} = 13\ N, \beta = \dfrac {2}{5} \dfrac {g}{R} = 5\times 10^{2} rad/ s^{2}$.

Question 10

How was it determined that a parsec is $ 3.26 $ light years?

Accepted Answer

Parallax is an effective way to measure distance to nearby stars because it relies on geometry. When astronomers use parallax, they are measuring how a star appears to move against its background. The unit parsec refers to the distance that an object would have to be from the Earth  to have a parallax angle of $ 1 $ arc-second.In the figure above, the angle, $ \alpha $ is the angle that is measured by the Earth on opposite sides of the sun. The parallax angle, $ p $ is half of this angle.$ p=\frac{1}{2}\alpha$If we defines $ p $ to be $ 1 $ arc-second, then our object will be $ 1 $ parsec away. Since light from the sun takes $ 8 $ minutes and $ 20 $ seconds to reach the Earth,. we know that;$ 1 AU=8.33 $ light minutesWe can use this information to convert our parsec into light years with the tangent formula.$ tan(p)=\frac{8.33 \quad light \quad minutes}{d}$Or;$ d=\frac{8.33 \quad light\quad minutes}{tan(p)}$If we convert $ p $  to radians, than we can use the small angle approximation, $ tan(\theta)\approx \theta$.$ 1 arc-second=4.85 \times 10^{-6} $ radiansPlugging this in for $ p $  and using the small angle approximation;$ d=\frac{8.33 \quad light\quad minutes}{4.85\times 10^{-6}}$=$ 1.72 \times 10^6 $ light-minutes=$ 3.26 $ light years

Basic Science

General Knowledge
15004 Views

How many feet are in a football field that is 100 yards?

What is the unit of viscosity? Please explain.

Two particles of equal mass (m) each move in a circle of radius (r) under the action of their mutual gravitational attraction the speed of the particle is

The dimensions of Planck's constant is

Is angular momentum equal to Inertia $\times ω$ and why?

Choose the correct answer from the alternatives given.
Time period is the time taken to complete one oscillation. This definition of time period is true for

How do vectors work in physics?

How was it determined that a parsec is $3.26$ light years?

Basic Science

General Knowledge 15004 Views

How many feet are in a football field that is 100 yards?

What is the unit of viscosity? Please explain.

Two particles of equal mass (m) each move in a circle of radius (r) under the action of their mutual gravitational attraction the speed of the particle is

The dimensions of Planck's constant is

Is angular momentum equal to Inertia ×ω and why?

Choose the correct answer from the alternatives given. Time period is the time taken to complete one oscillation. This definition of time period is true for

How do vectors work in physics?

How was it determined that a parsec is 3.26 light years?

General Knowledge
15004 Views

Is angular momentum equal to Inertia $\times ω$ and why?

Choose the correct answer from the alternatives given.
Time period is the time taken to complete one oscillation. This definition of time period is true for

How was it determined that a parsec is $3.26$ light years?