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Chapter 8: Problem 4

Which of the following statements is/are not true about gravitational constant? (a) Il has no units (b) It has same valuc in all systems of units (c) il is a foree (d) Il docs not depend upon the nature of medium in which the bodics lic

Short Answer

Expert verified
Statements (a) and (c) are not true.

Step by step solution

01

Analyze Statement (a)

Examine the statement 'It has no units'. The gravitational constant, denoted by \( G \), has units. In SI units, \( G \) is expressed in \( \text{N m}^2/ \text{kg}^2 \). This statement is incorrect since the gravitational constant does have units.
02

Analyze Statement (b)

Evaluate the statement 'It has same value in all systems of units'. The gravitational constant \( G \) is a universal constant and its numerical value remains consistent across different systems of units when proper conversion factors are used. This statement is true.
03

Analyze Statement (c)

Check the statement 'It is a force'. The gravitational constant \( G \) is not a force itself; rather, it is a constant used in the formula for gravitational force \( F = G \frac{m_1 m_2}{r^2} \). This statement is incorrect.
04

Analyze Statement (d)

Consider the statement 'It does not depend upon the nature of medium in which the bodies lie'. The gravitational constant \( G \) is indeed independent of the medium between the masses. It is a fundamental constant of nature. This statement is true.

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Key Concepts

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

Units of Measurement
When discussing the gravitational constant, it is crucial to consider its units of measurement. In the International System of Units (SI), which is the most widely used system in scientific work, the gravitational constant, denoted by \( G \), is measured in \( \text{N m}^2/ \text{kg}^2 \). This helps quantify the gravitational force between two masses in a clear and standardized way.
  • "N" stands for newtons, which is the unit of force.
  • "m" stands for meters, the standard unit of distance.
  • "kg" stands for kilograms, the standard unit of mass.
By combining these units, we can evaluate gravitational interactions accurately across different experiments and studies, ensuring consistency and reliability in scientific research.
Universal Constants
Universal constants, like the gravitational constant \( G \), play a vital role in physics. They are values that are constant in nature and hold the same value throughout the universe. The gravitational constant is essential in calculating gravitational force, which facilitates our understanding of how objects with mass interact.
These constants remain the same irrespective of the measure system employed, though their numerical value may appear differently if units change. By calibrating these constants across diverse measurement systems, we maintain consistency in scientific calculations.
Gravitational Force
Gravitational force is the attractive force that any two masses exert on each other. It is central to our understanding of phenomena ranging from falling objects to planetary orbits.
The formula for calculating gravitational force is:\[F = G \frac{m_1 m_2}{r^2}\]Here:
  • \( F \) is the gravitational force between two objects
  • \( m_1 \) and \( m_2 \) are the masses of the objects involved
  • \( r \) is the distance between the centers of the two masses
  • \( G \) is the gravitational constant
In this formula, \( G \) is not a force itself, but a critical factor that ensures the proportionality of force with the product of the two masses and the inverse square of their separation distance.
Medium Independence
An intriguing aspect of the gravitational constant \( G \) is its independence from the medium through which the gravitational force acts. Whether in a vacuum or any other environment, the value of \( G \) remains unchanged.
This characteristic underscores that gravitational interactions are fundamental forces that do not rely on a medium to propagate. This is in stark contrast to forces like electromagnetism, which can vary based on the medium's properties.
Therefore, \( G \) being a universally constant value implies that gravitational force remains consistent across different environments, reinforcing the universality and stability of gravitational laws.

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Most popular questions from this chapter

Statement-1 : It is possible to put an artificial satellite into orbit in such a way that it will always remain directly over New Delhi. Statement-2: To pul an artificial satullite into orbit such that it remains directly over head at a fixed location, its time period should be related to that of earth in the equatorial plane.

A solid sphere of uniform density and radius 4 units is located with its centre at the origin \(O\) of coordinates. Two spheres of equal radii 1 unit, with their centres at \(A(-2,0,0)\) and \(B(2,0,0)\) respectively, are taken out of the solid leaving behind spherical cavitics as shown in the figurc. Then, (a) the gravitational force due to this object at the origin is zero. (b) the gravitational force at the point \(B(2,0,0)\) is zero. (c) the gravitational potential is the same at all points of the circle \(z^{2}+y^{2}-36\) (d) the gravitational potential is same at all points of the circle \(y^{2}+z^{2}-4\)

Statement-1 : If carth were a uniform hollow sphere, work required to be done in moving a mass from one point to other inside the carth would be zero. Statement-2: The gravitational ficld inside a uniform hollow sphere is zero.

Which of the following statements is/are true for a stationary satellite of the carth? (a) I is stationary in spaco (b) Its time period is 24 hours (c) Its angular speed is cqual to that of carth about its own axis (d) It rovolves from west to cast

Three particles each having a mass of \(100 \mathrm{gm}\) are placed on the vertices of an equilateral triangle of side \(20 \mathrm{~cm}\). The work done in increasing the side of this triangle to \(40 \mathrm{~cm}\) is \(\left(G=6.67 \times 10^{\prime \prime} \mathrm{Nm}^{2} \mathrm{~kg}^{2}\right)\) (a) \(5.0 \times 10^{-12} \mathrm{~J}\) (b) \(2.25 \times 10^{-10} \mathrm{~J}\) (c) \(4.0 \times 10^{-11} \mathrm{~J}\) (d) \(6.0 \times 10^{-15} \mathrm{~J}\)
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