/*! 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} Problem 25 Statement-1: For a system of mas... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 25

Statement-1: For a system of masses, at some finite distance gravitational ficld can be zero but gravitational potential cannot. Statement-2 : Gravitational ficld is a vector quantity, while potential a scalar onc.

Short Answer

Expert verified
Both statements are true; Statement-2 explains Statement-1.

Step by step solution

01

Analyzing Statement-1

Statement-1 suggests that in a system of masses, the gravitational field can be zero at some points where the gravitational potential is not zero. To understand this, recall that the gravitational field is a vector quantity, and can cancel out if multiple masses are involved with forces in opposite directions, leading to a net field of zero. However, gravitational potential is a scalar quantity and is simply the algebraic sum of potentials from each mass; hence, it cannot be zero simply by cancelation.
02

Analyzing Statement-2

Statement-2 correctly identifies the nature of gravitational field and potential: the gravitational field is indeed a vector quantity, involving both magnitude and direction, while the gravitational potential is a scalar, having magnitude only without any direction.
03

Correlating Statements

Now, correlate the two statements. The first statement is logically derived from the facts mentioned in the second statement. Since fields are vectors, they can sum to zero if opposite in direction. In contrast, potentials, being scalar, would still sum to a non-zero value unless each contributing mass's potential is zero, which practically doesn't occur unless there are no masses.
04

Conclusion

Both statements are correct and Statement-2 is a valid explanation for Statement-1 since Statement-1 follows from the vector nature of gravitational fields and the scalar nature of potential.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vector and Scalar Quantities
Understanding the difference between vector and scalar quantities is crucial when studying gravitational concepts. Vectors are quantities that have both magnitude and direction. This means vectors tell you how much of something there is and which way it's going. Examples include velocity, force, and of course, the gravitational field.
Scalars, on the other hand, have only magnitude and lack any directional component. They are just amounts. Examples include temperature, speed, and gravitational potential.
  • The distinction is important in physics because it affects how different quantities interact and are calculated.
  • Vector quantities can cancel each other out if they are in opposite directions, but scalar quantities do not work this way.
Gravitational Field
The gravitational field is a fascinating concept that describes the gravitational force exerted per unit mass at any point in space. It's a vector quantity, meaning it has both a specific strength (magnitude) and a specific direction. The gravitational field around any object points towards the object itself.
When dealing with multiple masses, the fields from each mass can interact.
  • At certain points, these fields might cancel each other out if they are in opposite directions, resulting in a net gravitational field of zero.
  • This is possible because the vector components can negate each other's effects.
Gravitational Potential
Unlike the gravitational field, gravitational potential is a scalar quantity. It is a measure of the potential energy per unit mass that a mass would have at a certain position in a gravitational field. This potential is calculated by summing the potentials due to each mass, without considering the direction, because it is scalar.
  • The gravitational potential can never be zero purely through cancellation like vectors.
  • Instead, to get a zero potential, you must have no contribution from all surrounding masses, which is highly unlikely.
Vector Cancellation
Vector cancellation is an intriguing phenomenon where vectors can negate each other if they act in opposite directions.
Consider a point in space with forces in opposing directions; the forces' magnitudes can match perfectly, and their directions are opposite. In such cases, they cancel each other out, leading to a sum of zero.
This concept is vital when examining why gravitational fields at certain points might be zero despite multiple surrounding masses. The different gravitational fields exert just the right opposing forces such that their vector sum is nullified.
  • Scalar quantities, however, do not experience such cancellation.
Algebraic Sum of Potentials
The algebraic sum of potentials refers to how we calculate total gravitational potential in a region. For scalar quantities like potential, you simply add up all individual contributions from each source without considering their direction. Because they are scalars, potentials only increase or decrease based on magnitude, unaffected by vector direction rules.
This means even if you have opposing sources or directions, the potential sums up to a positive or negative value based solely on size.
  • Thereby, purely algebraic summation ensures potentials from multiple sources are always combined.
  • Differences in position or direction do not lead to cancellation as is possible with vector fields.

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

The magnitudes of the gravitational field at distances \(r_{1}\) and \(r_{2}\) from the centre of a unilorm sphere of radius \(R\) and mass \(M\) arc \(F_{1}\) and \(F_{2}\) respectively. Then (a) \(\frac{F_{1}}{F_{2}}-\frac{r_{1}}{r_{2}}\) if \(r_{1}R\) and \(r_{2}>R\) (c) \(\frac{F_{1}}{F_{2}}-\frac{r_{1}^{3}}{r_{2}^{3}}\) if \(r_{1}

Two satellites \(S_{1}\) and \(S_{2}\) revolve round a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 hour and 8 hours respectively. The radius of the orbit of \(S_{1}\) is \(10^{4} \mathrm{~km}\). When \(S_{2}\) is closest to \(S_{1}\), find (a) the specd of \(S_{2}\) relative to \(S_{1}\) and (b) the angular speed of \(\mathrm{S}_{2}\) as observed by an astronout in \(S_{1}\).

The figure represents an clliptical orbit of a planet around sun. The planet takes time \(T_{1}\) to travel from \(A\) to \(B\) and it takes time \(T_{2}\) to travel from \(C\) to \(D\). If the area \(C S D\) is double that of area \(A S B\), then (a) \(T_{1}-T_{2}\) (b) \(T_{1}-2 T_{2}\) (c) \(T_{1}-0.5 T_{2}\) (d) Data insufficient

Choose the wrong statements from the following (a) It is possible to shield a body from the gravitational field of another body by using a thick shiclding material between them. (b) The cacape velocity of a body is independent of the mass of the body and the angle of projection. (c) The acocleration due to gravily increases due to the rotation of the carth. (d) The gravitational force exeried by the earth on a body is greater than that exerted by the body on the carh.

A planet of mass \(m\) moves round the sun of mass \(M\) in a circular orbit of radius \(r\) with angular speed \(\omega .\) Another planet of mass \(2 m\) moves round the Sun in circular orbit of radius \(4 r\) with angular speed \(\omega^{\prime} .\) The ratio \(\frac{\omega}{\omega^{\prime}}\) is cqual to (a) 4 (b) \(\frac{1}{4}\) (c) 8 (d) \(\frac{1}{8}\)
See all solutions

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Read Explanation

Atoms and Radioactivity

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Dynamics

Read Explanation

Fields in Physics

Read Explanation

Physical Quantities And Units

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.