The expression for
g
on Earth and the acceleration due to gravity on the surface of the Moon is one-sixth that of acceleration due to gravity on Earth.
Answer to Problem 3AYK
Explanation of Solution
The expression for force of gravity on Earth according to Universal law of Gravitation is,
Here,
The expression for force of gravity or weight on Earth is,
Here,
The expression for acceleration due to gravity can be obtained by equating the two forces as both are gravitational forces acting on the object on Earth.
The expression for acceleration due to gravity or
Let
The value of
Substitute
The expression for acceleration due to gravity on moon is,
Here,
Substitute
The expression for the ratio of acceleration due to gravity on Moon and Earth is,
Substitute
Therefore, acceleration due to gravity on the surface of the Moon is
Conclusion:
Therefore, the expression for
Want to see more full solutions like this?
Chapter 3 Solutions
INTRO.TO PHYSICAL SCIENCE NSU PKG >IC<
- Find the magnitude of the gravitational force (in N) between a planet with mass 6.75 * 10 ^ 24 * kg and its moon, with mass 2.55 * 10 ^ 22 * kg if the average distance between 2.60 * 10 ^8 m. What is the moon's acceleration (in m /s ^ 2) toward the planet? What is the planet's acceleration (in m/s^ 2 ) toward the moon?arrow_forwardThe SI unit of G, the universal gravitation constant is ______________. A) N m2 kg2 B) N m2 kg-2 C) N m-2 kg-2 D) N m-2 kg2arrow_forwardFind the elevation h (km) where the weight of an object is 3/9 its weight on the surface of the earth. Use Me = 5.9742 × 1024 kg, G = 6.67 × 10−11 m3/(kg ·s2) and Re = 6378 km, respectively.arrow_forward
- Consider a human who weighs 862 N on Earth. What is the person's mass on Earth? And what is the same person's mass on Mars, where the acceleration due to gravity is 3.7 m/s2?arrow_forwardFind the resultant force on (a) the mass m1 = 0.197 kg and (b) the mass m2 = 0.106 kg in the figure below (the masses are isolated from the earth). Fm1 =________N Fm2 =________Narrow_forwardIf you are trying to find the acceleration of gravity using a mass pundit in with length I and period T, g= a.) T I/2p b.) T^2/(4p^2I) c.) 4p^2I/T^2 d.) 2pI/Tarrow_forward
- Determine the height habove the surface of a planet of radius R and mass M at which the gravitational field will be 60% of its surface value (express h in terms of R). [Hint: Strictly speaking, the acceleration due to gravity g is a function of the height h above planet’s surface, i.e., g = g(h). If the weight of a mass m at a height h is mg(h), then mg(h) = GMm/(R+h)2.] a) 0.6R b) 0.58R c) 0.29Rarrow_forwardIs the value of acceleration due to gravity (g) the same at the different places on Earth? Why?arrow_forwardThe gravitational acceleration constant gx on Planet X can be approximated by determining the acceleration of an object assuming Newton's Law of Universal Gravitation. If gx = 3.8 m/s^2 , G = 6.7 x 10^-11 Nm^2/kg^2, and Planet X's radius is 4000 km, what is the approximate mass of planet X? Give answer in kg.arrow_forward
- Suppose that a projectile of mass m moves in a verticalplane in the atmosphere near the surface of the earth underthe influence of two forces: a downward gravitationalforce of magnitude mg, and a resistive force FR that isdirected opposite to the velocity vector v and has magnitudek v2 (where v = |v| is the speed of the projectile;see Fig. 4.1.15). Show that the equations of motion of theprojectile are mx'' = -kvx' , my'' = -kvy' -mg,arrow_forwardWhich of the following statements about gravitational force, Fg , is not correct? a. Gravitational force is an attractive force only; it is never repulsive. b. Gravitational forces always exist in pairs of equal magnitude. c. The gravitational force between two objects depends on their separation. d. Gravitational force is the strongest of the fundamental forces.arrow_forwardOn a planet whose radius is 1.7 ✕ 107 m, the acceleration due to gravity is 47 m/s2. What is the mass of the planet (in kg)?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill