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Physics · GRAVITATION
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Physics · GRAVITATION
The gravitational force between two point masses \( m_1 \) and \( m_2 \) separated by distance \( r \) is \( F \). If the mass \( m_1 \) is increased by \( 100\% \), mass \( m_2 \) is decreased by \( 50\% \), and the distance between them is halved, the new gravitational force will be:
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In the given diagram, a point mass \( m \) is located at depth \( d \) from the Earth's surface. What fraction of the Earth's total mass \( M_E \) contributes to the gravitational force acting on this mass, assuming uniform density?
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The work done in lifting a particle of mass \( m \) from a distance \( r_1 \) to \( r_2 \) (where \( r_2 > r_1 > R_E \)) from the centre of the Earth of mass \( M_E \) is:
Read answer →Physics · GRAVITATION
Why is the historical Cavendish experiment often famously described as an experiment to 'weigh the Earth'?
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The Moon completes one revolution around the Earth in \( 27.3\text{ days} \) in an orbit of radius \( 3.84 \times 10^8\text{ m} \). If \( G = 6.67 \times 10^{-11}\text{ N m}^2\text{ kg}^{-2} \), the mass of the Earth calculated from this data is approximately:
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Given below are two statements: Statement I: For an orbiting satellite in an elliptical orbit, both the kinetic energy and potential energy vary from point to point along the orbit. Statement II: The total mechanical energy of an orbiting satellite in an elliptical orbit remains constant and is negative. In the light of the above statements, choose the most appropriate answer from the options given below:
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Four identical particles, each of mass \( m \), are placed at the vertices of a square of side \( l \). The work required to double each side of the square while maintaining its square configuration is:
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The escape speed from the surface of Earth is approximately \( 11.2\text{ km/s} \). If the acceleration due to gravity on the Moon is \( g/6 \) and its radius is \( R_E/4 \), the escape speed from the Moon's surface would be approximately:
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Given below are two statements: Statement I: A circle is a special case of an ellipse whose two foci merge into a single point. Statement II: Kepler's first law proposed that all planets move in exact circular orbits around a fixed central Sun. In the light of the above statements, choose the most appropriate answer from the options given below:
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A satellite of mass \( 400\text{ kg} \) is in a circular orbit of radius \( 2 R_E \) about the Earth. How much energy is required to transfer it into a circular orbit of radius \( 4 R_E \)? (Take \( g = 9.81\text{ m s}^{-2} \) and \( R_E = 6.37 \times 10^6\text{ m} \))
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A satellite of mass \( m \) is orbiting in a circular orbit of radius \( r \) around a planet of mass \( M \). What is the ratio of its kinetic energy \( K \), potential energy \( U \), and total mechanical energy \( E \)?
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In the diagram shown below, two fixed solid spheres have masses \( M \) and \( 4M \) and radii \( R \), with center-to-center distance \( 6R \). At the neutral point \( N \) located along the line joining their centers, what is the distance of \( N \) from the center of sphere of mass \( M \)?
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A body is projected vertically upwards from the surface of the Earth with a speed \( v_i = \sqrt{3} v_e \), where \( v_e \) is the escape speed from the Earth's surface. Its speed at an infinite distance from the Earth will be:
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A planet orbits the Sun in an elliptical path. The distance of the planet at perihelion is \( r_P \) and at aphelion is \( r_A \). If the linear speed of the planet at perihelion is \( v_P \), what is its linear speed \( v_A \) at aphelion?
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At what depth \( d \) below the surface of the Earth will the acceleration due to gravity become one-fourth of its value on the Earth's surface? (Assume the radius of Earth is \( R_E \))
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At what height \( h \) above the surface of the Earth does the acceleration due to gravity become \( \frac{g}{9} \), where \( g \) is the value of acceleration due to gravity on the Earth's surface and \( R_E \) is the Earth's radius?
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Assuming the Earth to be a homogeneous sphere of uniform density \( \rho \) and radius \( R_E \), the gravitational acceleration \( g(r) \) at a distance \( r \) inside the Earth (\( r < R_E \)) is proportional to:
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The work done in lifting a particle of mass \( m \) from a distance \( r_1 \) to \( r_2 \) (\( r_2 > r_1 \)) from the centre of the Earth of mass \( M_E \) along a vertical path is:
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A particle of mass \( m \) is placed inside a uniform solid sphere of mass \( M_E \) and radius \( R_E \) at a distance \( r = \frac{R_E}{4} \) from the centre. The gravitational force acting on the particle is:
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If the reference point of zero gravitational potential energy is chosen such that \( W(r \to \infty) = 0 \), the gravitational potential energy of a two-particle system with masses \( m_1 \) and \( m_2 \) separated by distance \( r \) is:
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Consider the following statements regarding an artificial satellite revolving in a circular orbit around the Earth: (A) The centripetal force is provided by the gravitational attraction of the Earth. (B) The linear speed of the satellite is directly proportional to the square root of its orbital radius. (C) The time period of revolution is independent of the mass of the satellite. (D) If the radius of the orbit is doubled, its orbital speed decreases by a factor of \( \sqrt{2} \). Choose the correct answer from the options given below:
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Two planets revolve around the Sun with semi-major axes in the ratio \( 1 : 4 \). What is the ratio of their orbital time periods?
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