/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q13-30P In Problem 1, What ratio m / M聽... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Q13-30P (page 381)

In Problem 1, What ratio m / Mgives the least gravitational potential energy for the system?

Short Answer

Expert verified

Ratio mMwhich gives least gravitational potential energy is 0.5

Step by step solution

01

The given data

  1. Mass of particle is M
  2. Mass of another particle is M - m
02

Understanding the concept of the energy

To find the ratio, use the formula for gravitational potential energy in which potential energy is proportional to the product of masses and inversely proportional to the distance between the masses.

Formula:

Potential Energy, U=-GMmr (i)

03

Calculation of ratio which gives least potential energy

Ratio of m / M which gives minimum potential energy using equation (i):

U=-GmM-mr

To find minimum potential energy,

dUdm=0-GM-2mr=0M-2m=0M=0.5mmM=0.5

Hence, the ratio at which we obtain least potential energy is 0.5

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Two20Kgspheres are fixed in place on a yaxis, one aty=0.40mand the other aty=鈭�0.40m. A 10 kg ball is then released from rest at a point on the xaxis that is at a great distance (effectively infinite) from the spheres. If the only forces acting on the ball are the gravitational forces from the spheres, then when the ball reaches the (x, y) point(0.30m,0),,what are (a) its kinetic energy and (b) the net force on it from the spheres, in unit-vector notation?

The Martian satellite Phobos travels in an approximately circular orbit of radius 9.4脳106mwith a period of7h39min .Calculate the mass of Mars from this information.

Question: A certain triple-star system consists of two stars, each of mass m , revolving in the same circular orbit of radius raround a central star of mass M (Fig. 13-54).The two orbiting stars are always at opposite ends of a diameter of the orbit. Derive an expression for the period of revolution of the stars.

A satellite orbits a planet of unknown mass in a circle of radius 2.0脳107m. The magnitude of the gravitational force on the satellite from the planet is F=80鈥�N.

(a) What is the kinetic energy of the satellite in this orbit?

(b) What would F be if the orbit radius were increased to3.0脳107m ?

In 1610, Galileo used his telescope to discover four prominent moons around Jupiter. Their mean orbital radiiaand periodsTare as follows:

(a) Plot log a (y-axis) against log T (x-axis) and show that you get a straight line.

(b) Measure the slope of the line and compare it with the value that you expect from Kepler鈥檚 third law.

(c) Find the mass of Jupiter from the intercept of this line with the y axis.
See all solutions

Recommended explanations on Physics Textbooks

Rotational Dynamics

Read Explanation

Atoms and Radioactivity

Read Explanation

Modern Physics

Read Explanation

Waves Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Electrostatics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.