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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