Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Physics

Mechanics

Easy

Question

A particle of mass m is thrown in a parabolic path towards earth having mass M and radius R. It comes to a greatest approach distance R/2 from surface of earth. Magnitude of total energy change required to make the particle moving in an elliptical path having eccentricity ½ with the greatest approach point either aphelion or perihelion are

$\frac{1}{3} \frac{G M m}{R}$
$\frac{1}{6} \frac{G M m}{R}$
$\frac{1}{2} \frac{G M m}{R}$
$\frac{G M m}{R}$

The correct answers are: $1 over 6 fraction numerator G M m over denominator R end fraction$ , $1 half fraction numerator G M m over denominator R end fraction$

By energy conservation, $v subscript A equals square root of 4 over 3 fraction numerator G M over denominator R end fraction end root$
(i) For aphelion point $v subscript R equals square root of fraction numerator G M over denominator 3 R end fraction end root$
$equals 1 half m open parentheses fraction numerator G M over denominator 3 R end fraction close parentheses minus 1 half m open parentheses fraction numerator 4 G M over denominator 3 R end fraction close parentheses equals negative 1 half fraction numerator G M m over denominator R end fraction$
(ii) For perihelion point $v subscript R equals square root of fraction numerator G M over denominator R end fraction end root$
$rightwards double arrow capital delta E equals 1 half m open parentheses fraction numerator G M over denominator R end fraction close parentheses minus 1 half m open parentheses fraction numerator 4 G M over denominator 3 R end fraction close parentheses equals negative 1 over 6 fraction numerator G M m over denominator R end fraction$

Related Questions to study

If a body is projected with a speed lesser than escape velocity, then

If a body is projected with a speed lesser than escape velocity, then

PhysicsMechanics

Figure shows the kinetic energy (E_k) and potential energy (E_p) curves for a two-particle system. Name the point at which the system is a bound system.

Figure shows the kinetic energy (E_k) and potential energy (E_p) curves for a two-particle system. Name the point at which the system is a bound system.

PhysicsMechanics

An artificial satellite moving in a circular orbit around the earth has a total energy E₀ . Its potential energy is

An artificial satellite moving in a circular orbit around the earth has a total energy E₀ . Its potential energy is

PhysicsMechanics

parallel

Two stars each of mass M and radius R are approaching each other for a head-on collision. They start approaching each other when their separation is r>>R. If their speeds at this separation are negligible, the speed v with which they collide would be

Two stars each of mass M and radius R are approaching each other for a head-on collision. They start approaching each other when their separation is r>>R. If their speeds at this separation are negligible, the speed v with which they collide would be

PhysicsMechanics

$text A satellite of mass end text straight m text is in a circular orbit of radius end text 2 R subscript straight F text about the earth. The energy required end text text to transfer it to a circular orbit of radius end text 4 R subscript E text is (where end text M subscript E text and end text R subscript E text is the mass and radius of end text t h e space e a r t h space r e s p e c t i v e l y right parenthesis$

$text A satellite of mass end text straight m text is in a circular orbit of radius end text 2 R subscript straight F text about the earth. The energy required end text text to transfer it to a circular orbit of radius end text 4 R subscript E text is (where end text M subscript E text and end text R subscript E text is the mass and radius of end text t h e space e a r t h space r e s p e c t i v e l y right parenthesis$

PhysicsMechanics

The orbital velocity of a satellite at a height R above the surface of Earth is v. The escape velocity from the location is

The orbital velocity of a satellite at a height R above the surface of Earth is v. The escape velocity from the location is

PhysicsMechanics

parallel

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is v. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is v. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

PhysicsMechanics

$text Two satellites end text S subscript 1 text and end text S subscript 2 text are revolving round a planet in coplanar and concentric circular orbit end text text of radii end text R subscript 1 text and end text R subscript 2 text in the same direction respectively. Their respective periods of revolution are end text 1 hr text and end text 8 hr text . The radius of the orbit of satellite end text S subscript 1 text is equal to end text 10 to the power of 4 km text . Find the relative speed end text text in kmph when they are closest. end text$

$text Two satellites end text S subscript 1 text and end text S subscript 2 text are revolving round a planet in coplanar and concentric circular orbit end text text of radii end text R subscript 1 text and end text R subscript 2 text in the same direction respectively. Their respective periods of revolution are end text 1 hr text and end text 8 hr text . The radius of the orbit of satellite end text S subscript 1 text is equal to end text 10 to the power of 4 km text . Find the relative speed end text text in kmph when they are closest. end text$

PhysicsMechanics

A satellite moves eastwards very near the surface of the Earth in equatorial plane with speed $open parentheses V subscript 0 close parentheses$ . Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If R = radius of the Earth and $omega$ be its angular speed of the Earth about its own axis. Then find the approximate difference in the two time period as observed on the Earth.

A satellite moves eastwards very near the surface of the Earth in equatorial plane with speed $open parentheses V subscript 0 close parentheses$ . Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If R = radius of the Earth and $omega$ be its angular speed of the Earth about its own axis. Then find the approximate difference in the two time period as observed on the Earth.

PhysicsMechanics

parallel

The little prince (the main character of the novel written by Antoine de Saint-Exupery) lives on the spherical planet named B-612, the density of which is 5200 kg/m³. The Little Prince noticed that if he quickens his pace. he feels himself lighter. When he reached the speed of 2m/s he became weightless, and began to orbit about the planet as a satellite. What is escape speed on the surface of planet?

The little prince (the main character of the novel written by Antoine de Saint-Exupery) lives on the spherical planet named B-612, the density of which is 5200 kg/m³. The Little Prince noticed that if he quickens his pace. he feels himself lighter. When he reached the speed of 2m/s he became weightless, and began to orbit about the planet as a satellite. What is escape speed on the surface of planet?

PhysicsMechanics

A satellite revolves in elliptical orbit around a planet of mass M. Its time period is T and M is at the centre of the path. The length of the major axis of the path is: (neglect the gravitational effect of other objects in space)

A satellite revolves in elliptical orbit around a planet of mass M. Its time period is T and M is at the centre of the path. The length of the major axis of the path is: (neglect the gravitational effect of other objects in space)

PhysicsMechanics

A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1 %, its speed will

A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1 %, its speed will

PhysicsMechanics

parallel

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is v. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is v. For a satellite orbiting at an altitude of half of the earth's radius, the orbital velocity is

PhysicsMechanics

The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K. E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is

The ratio of the K.E. required to be given to the satellite to escape earth's gravitational field to the K. E. required to be given so that the satellite moves in a circular orbit just above earth atmosphere is

PhysicsMechanics

$text Two satellites of masses end text m subscript 1 text and end text m subscript 2 open parentheses m subscript 1 greater than m subscript 2 close parentheses text are revolving round the earth in circular orbits end text text of radius end text r subscript 1 text and end text r subscript 2 open parentheses r subscript 1 greater than r subscript 2 close parentheses text respectively. Which of the following statements is true regarding end text text their speeds end text v subscript 1 text and end text v subscript 2 ?$

$text Two satellites of masses end text m subscript 1 text and end text m subscript 2 open parentheses m subscript 1 greater than m subscript 2 close parentheses text are revolving round the earth in circular orbits end text text of radius end text r subscript 1 text and end text r subscript 2 open parentheses r subscript 1 greater than r subscript 2 close parentheses text respectively. Which of the following statements is true regarding end text text their speeds end text v subscript 1 text and end text v subscript 2 ?$

PhysicsMechanics

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.