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A satellite moving in a circular orbit of radius R_{0} round t

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Solving time: 2 mins

A satellite moving in a circular orbit of radius $R_{0}$ round the Earth of mass $M$ and radius $R$ has angular velocity

\frac{GM}{R _{0}^{3}}

GMR_{0}^{3}

\frac{R _{0} ^{3}}{GM}

GMR_{0}^{2}

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Book:

IIT JEE Super Course in Physics Mechanics II (Pearson)

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A satellite moving in a circular orbit of radius

R_{0}

round the Earth of mass

M

and radius

R

has angular velocity

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Text solutionVerified

\frac{v _{0}^{2}}{R _{0}} = \frac{GM}{R _{0}^{2}}

ω^{2} = \frac{v _{0}^{2}}{R _{0}^{2}} = \frac{GM}{R _{0}^{3}} \Rightarrow ω = \frac{GM}{R _{0}^{3}}

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Practice questions from IIT JEE Super Course in Physics Mechanics II (Pearson)

Question 1

Medium

A projectile is fired vertically up from the Earth's surface, with a velocity equal to

3/ 4^{th}

of the escape velocity

v_{e}

from the surface of the Earth. The maximum distance of the projectile from centre of Earth is (radius of Earth = R)

$2 R$
$\frac{4}{3} R$
$\frac{16}{7} R$
$\frac{16}{9} R$

Topic:

Gravitation

Book:

IIT JEE Super Course in Physics Mechanics II (Pearson)

View solution

Question 2

Hard

Consider Earth as a uniform solid sphere. Consider Earth's rotation about its own axis. Speed of a point on equator is

v_{0}

. Escape velocity at pole is

v_{e}

. Point

P

is above pole. Accelerations due to gravity at

P

and on the surface of Earth at latitude

4 5^{\circ}

are equal. A stone dropped from P will hit Earth with speed. Case (i)

v^{'}

if we assume

g

to be constant and equal to the value at the surface of Earth. and Case (ii) v", otherwise.

v^{'} =

$\frac{v _{0}}{2}$
$\frac{v _{0}}{2}$
$2 v_{0}$
$2 v_{0}$

Topic:

Gravitation

Book:

IIT JEE Super Course in Physics Mechanics II (Pearson)

View solution

Question 3

Medium

A body falls from rest on to the Earth vertically with a speed of

\frac{2}{5} v_{esc}

. It must have travelled a distance of (

R =

radius of Earth)

$2 R$
$3 R$
$4 R$
$5 R$

Topic:

Gravitation

Book:

IIT JEE Super Course in Physics Mechanics II (Pearson)

View solution

Question 4

Medium

A

and

B

are of identical masses and radii.

A

is a spherical shell,

B

a solid sphere.

P

and

Q

are two points on the line joining centres and located within

A

and

B

respectively and at equal distances from the respective centres. Comparing the magnitudes of gravitational fields at

P

and

Q

.

Comparing the magnitudes of gravitational potentials at

P

and

Q

they are equal
more at $P$
more at $Q$
any of above is possible.

Topic:

Gravitation

Book:

IIT JEE Super Course in Physics Mechanics II (Pearson)

View solution

Practice more questions from Gravitation

Question 1

Medium

A body is weighed by a spring balance to be

1.000 kg

at the north pole. How much will it weight at the equator? Account for the earth's rotation only. Take

g_{pole} = 9.830 m / s^{2}

. and

R_{e} = 6400 km

Topic:

Gravitation

Book:

Physics Galaxy Mechanics Vol 1 (Ashish Arora)

View solution

Question 2

Easy

A tank of size

10 m \times 10 m \times 10 m

is full of water and built on the ground. If

g = 10 m s^{- 2}

, the potential energy of the water in the tank is

$5 \times 10^{7} J$
$1 \times 10^{8} J$
$5 \times 10^{4} J$
$5 \times 10^{5} J$

Topic:

Gravitation

View 3 solutions

Question 3

Medium

A satellite

S

is moving in an elliptical orbit around earth. The mass of the satellite is very small compared to the mass of the earth?

The acceleration of $S$ is always directed towards the centre of the earth
The angular momentum of $S$ about the centre of the earth changes in direction but its magnitude remains constant
The total mechanical energy of $S$ varies periodically with time
The linear momentum of $S$ remains constant in magnitude

Topic:

Gravitation

Book:

Master Resource Book in JEE Main Physics (Arihant)

View 15 solutions

Question 4

Medium

The change in potential energy when a body of mass

m

is raised to a height

n R

from the centre of earth (

R =

radius of earth)

$mgR \frac{( n - 1 )}{n}$
$nm g R$
$m g R \frac{n ^{2}}{n ^{2} + 1}$
$mgR \frac{n}{n + 1}$

Topic:

Gravitation

Book:

Master Resource Book in JEE Main Physics (Arihant)

View 10 solutions

Practice questions on similar concepts asked by Filo students

Question 1

Texts: Can you please solve this on a sheet of paper by hand? I would really appreciate it, photo attached. I have an exam soon and it would help a lot. 4. Coherent states of the quantum harmonic oscillator Consider a quantum harmonic oscillator with mass m, frequency ω, and length scale a₀ = ℏ/(mw). By definition, the coherent state with parameter α is the normalized eigenstate of the annihilation operator â, with eigenvalue α. â|α⟩ = α|α⟩ (1) a) Show that the following formula |α⟩ = e^(-|α|²/2) * ∑(n=0 to ∞) (α^n / √(n!)) |n⟩ (2) does satisfy the definition 1 of a coherent state. Moreover, show that this coherent state is normalized. Hint: The action of the annihilation operator on the energy eigenstates |n⟩ with n quanta of energy is given by â|n⟩ = √n|n-1⟩ [6 marks] b) From equation (2), show the following overcompleteness identity for the coherent states: ∫(|α⟩⟨α|) d²α = 1. Hint: The energy eigenstates are orthonormal. [4 marks] c) Show that the probability that a given coherent state |α⟩ is measured to contain n quanta of energy is equal to |⟨n|α⟩|² = e^(-|α|²) * (|α|²)^n / n! (n = 0, 1, 2, ...) [4 marks] d) Using the above formula, compute the expectation values ⟨α|N|α⟩ and ⟨α|N̂α⟩, where N̂ is the number operator, defined by N̂ = ∑(n=0 to ∞) n|n⟩⟨n|. [6 marks] Hint: To compute N̂², recall that the energy eigenstates are orthonormal.

Topic:

Physics

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Question 2

A long cylinder of aluminum of radius

R

meters is charged so that it has a uniform charge per unit length on its surface of

λ .

(a) Find the electric field inside and outside the cylinder. (b) Plot electric field as a function of distance from the center of the rod.

Topic:

Physics

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Question 3

Determine the maximum theoretical speed that may be achieved over a distance of

100 m

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Topic:

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Question 4

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Topic:

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Question Text	A satellite moving in a circular orbit of radius $R_{0}$ round the Earth of mass $M$ and radius $R$ has angular velocity
Topic	Gravitation
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	94