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Gravitation: Force inversely proportional to cube of distance.

Q- Consider an object of mass m, moving in a circular orbit, subject to a central attractive for F whose magnitude is given by F(r) = h/r3.

(a)What are the dimensions of h?

(b) Show that the angular momentum for the motion is uniquely determined by h and m.

(c) What is the resulting relatio…

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Gravitation

Q- The earth orbits the sun at a distance of about 1.5*1011 m, in about 365 days(3.15*107 s).

(a) What is the earth’s speed along its orbital path?

(b) If the mass of the earth is 6*1024 kg, find the force exerted on it by the sun.

(c) What is the mass of the sun?

Solution:

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Gravitation: Earth's Orbit

Q- The earth orbits the sun at a distance of about 1.5*1011 m in about 365 days (3.15*107 s).

(a) What is the earth’s speed along its orbital path?

(b) If the mass of the earth is 6*1024 kg, find the force exerted on it by the sun to keep it in orbit.

(c) What must be the mass of the sun to exe…

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Second Pendulum

Q- A second pendulum is one that moves through its equilibrium position once each second. The period of the pendulum is precisely 2s. The length of a second pendulum is 0.9927 m at Tokyo Japan and 0.9942 m at Cambridge England. What is the ratio of the free-fall accelerations at these two locations?

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Gravitation: Acceleration Due To Gravity

Q- Calculate the acceleration due to gravity at a height of 8.848 km from surface of the earth.

Solution:

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Gravitation

Q- Using mass of earth, distance between sun and earth and gravitation constant as given in your text, calculate mass of sun.

Solution:

 

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Gravitation: Potential Energy

Q- A body is projected vertically with a velocity of 6 km/s. Find the maximum height reached by projectile.

Solution:

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Gravitation

Q- Sketch graphs of total mechanical, potential and kinetic energy verses time, on the same paper, for  

(a)  a 0.5 kg metal ball dropped from rest falling from point A to B in 5 second under gravity. (g = 10 m/s2)  

(b) a 5.0g sheet of paper falling with terminal velocity 1 m/s from point A …

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Gravitation: Orbital Speed

Q- A Star S have two planets A and B. Planet A has average orbital radius three times as big as planet B. If planet A orbits S in 2 earth years,

(a) How long is a year for the resident of planet B

(b) What is linear orbital speed of planet B, if the average radius of A is 3*1011 m. 

Solution:

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Gravitation

Q- A particle is projected from the surface of the earth with a speed twice of the escape speed.  Neglecting air resistance, find its speed when it is far away from the earth. 

Solution:

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Gravitation

Q- A straight tunnel is dug through the earth (not passing through the center). Show that neglecting any resistive force the motion of an object inside the tunnel is simple harmonic motion and find the expression for time period of the motion.

Solution:

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Gravitation: Escape Velocity

Q- A particle is projected from the surface of the earth with speed twice the escape speed. When it is very far from the earth, what is its speed?

Solution:

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Kepler's Law

Q- A distant star has two planets following circular orbits about the star with one planet four times the distance from the star as the other planet. If the planet closer to the star has a period of 2 years, determine the period of the planet farther from the star.

Solution:

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Gravitation

Q- At what altitude above the Earth's surface would your weight be three-fourths of what it is at the Earth's surface? Assume re = 6.371*103 km.

Solution:

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Gravitation

Q- Four identical point particles (each having mass m=5000kg) are located at the points (-2,0), (0,8), (6,0) and (0,3) in the xy plane. All positions are measured in meters. Determine the magnitude of the total gravitational force on the particle located at (6,0) due to the other three particles.

S…

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Gravitation

Q1- Neutron stars are extremely dense objects with a mass comparable to the mass of the sun but a radius of only several thousand meters. Consider a neutron star of mass M = 1.99*1030 kg and a radius of R = 10.2 km.

(a) What is the gravitational acceleration near the surface of the star?

(b) If an…

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Gravitation

(a) A space explorer comes across a spherical planet with a small moon in orbit around it. He observes that the moon completes one full orbit every 33 Earth days and moves at a distance R = 390 million m from the center of the planet. What is the mass of the planet? (One earth day =86400 s)

(b) U…

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