This question tests the understanding of Newton's Law of Universal Gravitation. We need to analyze how the gravitational force changes when one of the masses is doubled, while the other mass and the distance between them remain constant.
Recall Newton's Law of Universal Gravitation: The gravitational force \(F\) between two bodies with masses \(m_1\) and \(m_2\), separated by a distance \(r\), is given by the formula:
\[ F = G \frac{m_1 m_2}{r^2} \]where \(G\) is the universal gravitational constant.
Identify the initial conditions: Let the initial masses be \(m_1\) and \(m_2\), and the distance be \(r\). The initial gravitational force is \(F_1 = G \frac{m_1 m_2}{r^2}\).
Identify the changed conditions: According to the problem, one of the masses is doubled. Let's assume \(m_1\) is doubled, so the new mass is \(m_1' = 2m_1\). The other mass \(m_2\) and the distance \(r\) remain unchanged.
Calculate the new gravitational force: Substitute the new mass into the formula:
\[ F_2 = G \frac{(2m_1) m_2}{r^2} \]Compare the new force with the original force:
\[ F_2 = 2 \left( G \frac{m_1 m_2}{r^2} \right) \]Since \(F_1 = G \frac{m_1 m_2}{r^2}\), we can write:
\[ F_2 = 2 F_1 \]This shows that the new gravitational force \(F_2\) is exactly double the original gravitational force \(F_1\).
C) Become exactly double its original value. As derived from Newton's Law of Universal Gravitation, doubling one of the masses directly doubles the gravitational force, assuming other parameters remain constant.
The question asks about the direction of the gravitational force between two masses as described by Newton's Law of Gravitation. Understanding the fundamental definition of this law is key to answering correctly.
B) The straight line joining the centres of the two masses. This is a direct statement from Newton's Law of Universal Gravitation. The gravitational force is always an attractive force acting along the line connecting the centers of the two interacting masses.
The question asks about the nature and magnitude of the gravitational force between two everyday objects. We need to apply Newton's Law of Universal Gravitation to determine the characteristics of this force.
D) Extremely small (practically negligible) because of their relatively tiny masses, though never exactly zero
This option accurately describes the gravitational force between two everyday objects. The masses of books are very small compared to astronomical bodies, leading to a minuscule gravitational force. However, as long as objects possess mass, there will always be a non-zero gravitational attraction between them, no matter how small.
The question asks for the specific term used to describe the acceleration experienced by an object falling solely under the influence of Earth's gravity. We need to identify the correct physics term from the given options.
Correct Option: D) The acceleration produced in a body falling freely under the influence of only the Earth's gravitational pull is universally known as the acceleration due to gravity, denoted by \(g\). Its approximate value near the Earth's surface is \(9.8 \, \text{m/s}^2\).
The question asks for the standard, average value of acceleration due to gravity (g) at the Earth's surface. This is a fundamental constant in physics, especially in mechanics and gravitation, and its value is widely known.
B) 9.8 m/s^2 is the internationally recognized standard average value for the acceleration due to gravity at the Earth's surface.
To define the weight of an object, we need to understand the fundamental concepts of mass, gravity, and force in physics. Weight is a measure of the gravitational force acting on an object, distinct from its mass.
C) The force with which the Earth (or any other planet) attracts the object towards its centre, equal to the object's mass multiplied by the local acceleration due to gravity.
This option accurately defines weight as a force caused by gravitational attraction, and correctly states its calculation as the product of mass and local acceleration due to gravity (\(W = m \times g\)). This force is directed towards the center of the celestial body exerting the gravitational pull.