Practice Quiz on Gravitation

Transcription

1 Practice Quiz on Gravitation 1 The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of m What is the mass of planet Nutron? a kg b kg c kg d kg e kg 2 Two stars of masses M and 6M are separated by a distance D Determine the distance (measured from M) to a point at which the net gravitational force on a third mass would be zero a 041 D b 033 D c 037 D d 029 D e 014 D 3 A satellite is in a circular orbit about the Earth at an altitude at which air resistance is negligible Which of the following statements is true? a There is only one force acting on the satellite b There are two forces acting on the satellite, and their resultant is zero c There are two forces acting on the satellite, and their resultant is not zero d There are three forces acting on the satellite e None of the preceding statements are correct

2 4 Three 50-kg masses are located at points in the xy plane, as shown What is the magnitude of the resultant force (caused by the other two masses) on the mass at x = 040 m, y = 0? y 30 cm a N b N c N d N e N 40 cm 5 What is the gravitational force on a 20-kg satellite circling the Earth (radius = m, mass = kg) with a period of 50 h? a 88 N b 55 N c 36 N d 98 N e 18 N x 6 A spacecraft (mass = m) orbits a planet (mass = M) in a circular orbit (radius = R) What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible? a GmM/(4R) b GmM/R c GmM/(2R) d GmM/(3R) e 2GmM/(5R)

3 7 An object is released from rest at a distance h above the surface of a planet (mass = M, radius = R < h) With what speed will the object strike the surface of the planet? Disregard any dissipative effects of the atmosphere of the planet a b c d e 2GMh R( R + h) R ( h R) Rh R + h R + h 8 An object is released from rest when it is a height h above the surface of a planet of mass M and radius R What is the speed of the object just before striking the surface of the planet? Neglect any air resistance Let h = m, R = m, and M = kg a 78 km/s b 35 km/s c 54 km/s d 69 km/s e 48 km/s 9 Planet Roton has a mass of kg and a radius of m With what speed should a space probe be launched from the surface of Roton so as to achieve a maximum distance of m from the center of Roton? a 42 km/s b 39 km/s c 30 km/s d 34 km/s e 60 km/s 10 What is the escape speed from a planet of mass M and radius R if M = kg and R = m? a 55 km/s b 42 km/s c 52 km/s d 48 km/s e 37 km/s

4 11 Planet Zero has a mass of kg and a radius of m A 10-kg space probe is launched vertically from the surface of Zero with an initial kinetic energy of J What maximum distance from the center of Zero is achieved by the probe? a m b m c m d m e m 12 A satellite is placed in a geosynchronous orbit In this equatorial orbit with a period of 24 hours, the satellite hovers over one point on the equator Which statement is true for a satellite in such an orbit? a There is no gravitational force on the satellite b There is no acceleration toward the center of the Earth c The satellite is in a state of free fall toward the Earth d There is a tangential force that helps the satellite keep up with the rotation of the Earth e The force toward the center of the Earth is balanced by a force away from the center of the Earth 13 Which of the following quantities is conserved for a planet orbiting a star in a circular orbit? Only the planet itself is to be taken as the system; the star is not included a Momentum and energy b Energy and angular momentum c Momentum and angular momentum d Momentum, angular momentum and energy e None of the above 14 The figure below shows a planet traveling in a clockwise direction on an elliptical path around a star located at one focus of the ellipse When the planet is at point A, A STAR a its speed is constant b its speed is increasing c its speed is decreasing d its speed is a maximum e its speed is a minimum

5 15 The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse When the planet is at point A, STAR A a its speed is constant b its speed is increasing c its speed is decreasing d its speed is a maximum e its speed is a minimum 16 The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse When the planet is at point A, A STAR a its speed is decreasing b its angular momentum is increasing c the gravitational force does no work on the planet d all of the above are correct e none of the above is correct 17 Three galaxies, each of mass M = kg, lie in a plane at the corners of an equilateral triangle with sides of m length The magnitude of the force the other two galaxies exert on each galaxy is a N b N c N d N e N

6 18 When two solid spheres of the same material and same radius r are in contact, the magnitude of the gravitational force each exerts on the other is directly proportional to a r b r 2 c r 3 d r 4 e r 6 19 Suppose the gravitational force of the Earth on a body was F = KM Em What escape velocity v e would a body need to escape the gravitational field of the Earth? a v e 2R E 2 b v e R E 2 c v e 2R E d v e R E e v e 20 Carla and Jenny are arguing about whether or not it is possible to escape the gravitational field of the Earth Carla shows Jenny the system below where mass m is r E (not the Earth s radius) distant from Earth and r P (not planet P s radius) distant from planet P Carla states that the mass m has escaped if F P on m = F E on M Which one, if either, is correct, and why? a Carla, because the total gravitational force on m is zero at that point b Carla, because there is no gravitational force from Earth on m at that point c Carla, because there is no gravitational force on m from Earth when r > r E d Jenny, because there is a gravitational force on m from Earth no matter how great the distance from the Earth e Jenny, because the gravitational force from the Earth can only be blocked by a body that is larger than the Earth r 3

7 1 d 2 d 3 a 4 d 5 c 6 c 7 a 8 d 9 c 10 b 11 d 12 c 13 b 14 c 15 c 16 e 17 c 18 d 19 b 20 d