Q4. (a) If r is the radius of the Earth, calculate the value of the Gravitational Potential at a distance of r from the Earths centre. (b) A black hole is defined as a body in space whose escape velocity is equal to or greater than the speed of light. An observed stellar object has a mass equal to 4 x 1030 kg and a radius of 2.9 km. I. Using appropriate physics prove that this stellar object can be classified as a black hole. II. What is the acceleration due to gravity on the surface of the object? (c) A woman is standing on the moon. By what factor would her weight increase if she were standing on the Earth as compared to the Moon?

Nothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00×10^8 m/s, making all escape impossible. What is the radius of the event horizon for a black hole with a mass 3.5 times the mass of the sun?

Around 2.5 centuries ago, several physicists of the time came up with the notion of a dark star.  This was a star so dense, with so much gravity, that not even light could escape.  The calculations used Newtonian mechanics.  In class, we calculated the escape speed from the surface of the earth or the distance from the sun, and the mass of the planet or star. Here, the process is partially reversed.  Calculate the dark star radius from the mass of the star and the escape speed.  Answer in kilometers. c = 3*108 m/s M = 3.2*1030 kg G = 2/3 * 10-10 N*m2/kg2

In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational constant G uses lead spheres with masses of 1.20 kg and 12.0 g whose centers are separated by about 4.90 cm. Calculate the gravitational force between these spheres, treating each as a particle located at the center of the sphere. Need Help? Master It Read It

The International Space Station, which has a mass of 4.94×105 kg, orbits 258 miles above the Earth's surface, and completes one orbit every 94.3 minutes. What is the kinetic energy of the International Space Station in units of GJ (109 Joules)? (Note: don't forget to take into account the radius of the Earth!) Enter answer here GJ

A 2000 kg lunar lander is in orbit 30 km above the surface of the moon. It needs to move out to a 500 km -high orbit in order to link up with the mother ship that will take the astronauts home. Part A How much work must the thrusters do? Express your answer with the appropriate units. μА Value Units ?

Question: Three identical 5.6 kg spheres are located at 3 of the 4 corners (top left, top right, and bottom right) of a square whose sides are 2.8 m in length. How much work must be done on the gravitational field produced by the spheres in order to remove the top right sphere (place it at infinity)? Assume that the 2 spheres that are left behind (top left, bottom right) remain located on opposite corners of the square. A) 1.50 x 10-9 J B) 5.34 x 10-10 J C) 1.89 x 10-10 J D) 2.67 x 10-10 J E) 5.29 x 10-10 J OA E B. C.

You are the pilot of a spacecraft intended for travel at very high speeds. Before leaving you measure the spacecraft to be 31.4 m long and have a mass of 5.28 x 104 kg. During your travel, you pass a planet and exchange information with an observer on the planet. You are told that your spacecraft has been measured to be 28.6 m long. a. How fast is your spacecraft travelling with respect to the planet? b. You are told there is a nearby planet that is stationary with respect to the first planet. The observer on the first planet says it will take you 25 s to reach the nearby planet. How far away does your co-pilot on the spacecraft say the nearby planet is? c. How much energy was required to accelerate your spacecraft to this speed?

10:24 P 62% ACSEE Physics - F5 - T2 - Mechanics.pdf Gravitational Potential of the Earth. Gravitational Field Strength of the Earth. How are the above quantities in and related? • (1999) Show that the total energy of a satellite in a circular orbit equals half its potential energy. • (1999) Calculate the height above the Earth's surface for a satellite in a parking orbit. • (1999) What would be the length of a day if the rate of rotation of the Earth were such that the acceleration of gravity g =0 at the equator? • (2007) Evaluate the work done by the Earth's gravitational force and by the tension in the string as the ball moves from its highest to its lowest point. • (2007) Two small spheres each of mass 10g are attached to a light rod 50 cm long. The system Is set into oscillation and the period of torsional oscillation is found to be 770 seconds. To produce maximum torsion to the system two large spheres each of mass 10 kg are placed near each suspended the distance between the…

Black holes are difficult to observewith telescopes because they, bydefinition, don’t emit or reflect any light. They can be found by look-ing for other nearby objects orbit-ing them, however. Here is a dia-gram of a star in a circular orbit around a black hole. a. The period of the star’s orbit is 90 days, and its orbital radius around the black hole isobserved to be 3.6 : ×10^11 m. Find the orbital velocity of the star in units of m/s. (You need to convert 90 days to seconds, first). The circumference of a circle is 2πr.  b. The mass of the star is known to be 4 × 10^30 kg. Find the centripetal acceleration of thestar and the strength of the gravitational force on the star.  c. Find the mass of the black hole.