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Page 1 Introductory Exercise 10.3 Q 1. The velocity of a particle is just equal to its escape velocity . Under such situation the total mechanical energy of the particle is zero. Is this statement true or false? Q 2. What is the kinetic energy needed to project a body of mass m from the surface of earth to infinity. Radius of earth is R and acceleration due to gravity on earth's surface is g. Q 3. Two particles of masses 20 kg and 10 kg are initially at a distance of 1.0 m. Find the speeds of the particles when the separation between them decreases to 0.5 m, if only gravitational forces are acting. Q 4. A particle is fired vertically upward with a speed of 15 km/s. Find the speed of the particle when it goes out of the earth's gravitational pull. Q 5. Show that if a body be projected vertically upward from the surface of the earth so as to reach a height nR above the surface : (i) the increase in its potential energy is n mgR n1 ?? ?? ? ?? , (ii) the velocity with which it must be projected is 2ngR n1 ? , where R is die radius of the earth and m the mass of body. Solutions 1. Escape velocity is given to overcome the potential barrier and just free the particle from a system, such that its total mechanical energy is just zero at infinity. So, the statement is true. 2. 3. Page 2 Introductory Exercise 10.3 Q 1. The velocity of a particle is just equal to its escape velocity . Under such situation the total mechanical energy of the particle is zero. Is this statement true or false? Q 2. What is the kinetic energy needed to project a body of mass m from the surface of earth to infinity. Radius of earth is R and acceleration due to gravity on earth's surface is g. Q 3. Two particles of masses 20 kg and 10 kg are initially at a distance of 1.0 m. Find the speeds of the particles when the separation between them decreases to 0.5 m, if only gravitational forces are acting. Q 4. A particle is fired vertically upward with a speed of 15 km/s. Find the speed of the particle when it goes out of the earth's gravitational pull. Q 5. Show that if a body be projected vertically upward from the surface of the earth so as to reach a height nR above the surface : (i) the increase in its potential energy is n mgR n1 ?? ?? ? ?? , (ii) the velocity with which it must be projected is 2ngR n1 ? , where R is die radius of the earth and m the mass of body. Solutions 1. Escape velocity is given to overcome the potential barrier and just free the particle from a system, such that its total mechanical energy is just zero at infinity. So, the statement is true. 2. 3. = 1.63 × 10 5 m/s = 33 × 10 5 m/s 4. = 10 km/s 5. (i) (ii) Introductory Exercise 10.4 Q 1. If a body is released from a great distance from the centre of the earth, find its velocity when it strikes the surface of the earth. Take R = 6400 km. Q 2. What quantities are constant in planetary motion? Q 3. Two satellites A and B of the same mass are orbiting the earth at altitudes R and 3R respectively, where R is the radius of the earth. Taking their orbits to be circular obtain the ratios of their kinetic and potential energies. Q 4. If a satellite is revolving close to a planet of density ? with period T, show that the quantity ?T 2 is a universal constant. Q 5. A satellite is revolving around a planet in a circular orbit. What will happen, if its speed is increased from v0 to: Page 3 Introductory Exercise 10.3 Q 1. The velocity of a particle is just equal to its escape velocity . Under such situation the total mechanical energy of the particle is zero. Is this statement true or false? Q 2. What is the kinetic energy needed to project a body of mass m from the surface of earth to infinity. Radius of earth is R and acceleration due to gravity on earth's surface is g. Q 3. Two particles of masses 20 kg and 10 kg are initially at a distance of 1.0 m. Find the speeds of the particles when the separation between them decreases to 0.5 m, if only gravitational forces are acting. Q 4. A particle is fired vertically upward with a speed of 15 km/s. Find the speed of the particle when it goes out of the earth's gravitational pull. Q 5. Show that if a body be projected vertically upward from the surface of the earth so as to reach a height nR above the surface : (i) the increase in its potential energy is n mgR n1 ?? ?? ? ?? , (ii) the velocity with which it must be projected is 2ngR n1 ? , where R is die radius of the earth and m the mass of body. Solutions 1. Escape velocity is given to overcome the potential barrier and just free the particle from a system, such that its total mechanical energy is just zero at infinity. So, the statement is true. 2. 3. = 1.63 × 10 5 m/s = 33 × 10 5 m/s 4. = 10 km/s 5. (i) (ii) Introductory Exercise 10.4 Q 1. If a body is released from a great distance from the centre of the earth, find its velocity when it strikes the surface of the earth. Take R = 6400 km. Q 2. What quantities are constant in planetary motion? Q 3. Two satellites A and B of the same mass are orbiting the earth at altitudes R and 3R respectively, where R is the radius of the earth. Taking their orbits to be circular obtain the ratios of their kinetic and potential energies. Q 4. If a satellite is revolving close to a planet of density ? with period T, show that the quantity ?T 2 is a universal constant. Q 5. A satellite is revolving around a planet in a circular orbit. What will happen, if its speed is increased from v0 to: (a) 0 1.5v (b) 2v0 Solutions 1. ?K = ?U × 10 3 m/s = km/s = 11.2 km/s 2. In planetary motion areal velocity, i.e., angular momentum and total mechanical energy is conserved. 3. 4. For = constant 5. (a) While, so, the satellite will not escape from the planet, rather it will revolve in elliptical orbit. Page 4 Introductory Exercise 10.3 Q 1. The velocity of a particle is just equal to its escape velocity . Under such situation the total mechanical energy of the particle is zero. Is this statement true or false? Q 2. What is the kinetic energy needed to project a body of mass m from the surface of earth to infinity. Radius of earth is R and acceleration due to gravity on earth's surface is g. Q 3. Two particles of masses 20 kg and 10 kg are initially at a distance of 1.0 m. Find the speeds of the particles when the separation between them decreases to 0.5 m, if only gravitational forces are acting. Q 4. A particle is fired vertically upward with a speed of 15 km/s. Find the speed of the particle when it goes out of the earth's gravitational pull. Q 5. Show that if a body be projected vertically upward from the surface of the earth so as to reach a height nR above the surface : (i) the increase in its potential energy is n mgR n1 ?? ?? ? ?? , (ii) the velocity with which it must be projected is 2ngR n1 ? , where R is die radius of the earth and m the mass of body. Solutions 1. Escape velocity is given to overcome the potential barrier and just free the particle from a system, such that its total mechanical energy is just zero at infinity. So, the statement is true. 2. 3. = 1.63 × 10 5 m/s = 33 × 10 5 m/s 4. = 10 km/s 5. (i) (ii) Introductory Exercise 10.4 Q 1. If a body is released from a great distance from the centre of the earth, find its velocity when it strikes the surface of the earth. Take R = 6400 km. Q 2. What quantities are constant in planetary motion? Q 3. Two satellites A and B of the same mass are orbiting the earth at altitudes R and 3R respectively, where R is the radius of the earth. Taking their orbits to be circular obtain the ratios of their kinetic and potential energies. Q 4. If a satellite is revolving close to a planet of density ? with period T, show that the quantity ?T 2 is a universal constant. Q 5. A satellite is revolving around a planet in a circular orbit. What will happen, if its speed is increased from v0 to: (a) 0 1.5v (b) 2v0 Solutions 1. ?K = ?U × 10 3 m/s = km/s = 11.2 km/s 2. In planetary motion areal velocity, i.e., angular momentum and total mechanical energy is conserved. 3. 4. For = constant 5. (a) While, so, the satellite will not escape from the planet, rather it will revolve in elliptical orbit. (b) As, while, v =2vo i.e., the satellite will escape.Read More
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1. What is the formula to calculate the gravitational force between two objects? 
2. How does the gravitational force between two objects change if the distance between them is doubled? 
3. What happens to the gravitational force if the mass of one object is doubled while keeping the other object's mass constant? 
4. Can the gravitational force between two objects ever be zero? 
5. How does the gravitational force vary with the mass of the objects involved? 
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