Study Material
GRAVITATION
Very Short Answer Questions
Q1. What velocity will you give to a donkey and a squirrel respectively so that both escape earth's gravitational field?
Q2. Earth is continuously pulling moon towards its center. Why does not moon fall on the earth.
Q3. How much energy is required by a satellite to keep it orbiting? (neglect the atmospheric resistance). Justify.
Q4. If Gravitational force acts in proportion to their masses, then why doesn't a heavy body fall faster than a lighter body.
Q5. When an apple falls towards the earth, the Earth also moves up to meet the apple. Is the statement true or false? Justify your answer.
Q6. Why does an astronaut feel a sense of weightlessness in a satellite revolving around the earth?
Q7. Hydrogen escapes faster than oxygen from earth's surface. Why?
Q8. Two masses of \(20\,\mathrm{kg}\) and \(30\,\mathrm{kg}\) are placed \(5\,\mathrm{m}\) apart. Find the force of attraction between them.
Q9. Calculate the potential energy of a satellite of mass \(1000\,\mathrm{kg}\) revolving at a height of \(500\,\mathrm{km}\) from the earth's surface.
Q10. As we move from one planet to another how does the mass and weight of a body change?
Q11. Keeping the length of the simple pendulum constant will the time period be same on all the planets? Justify
Q12. What are the factors that make the value of 'g' the least at the equator and maximum at the poles?
Q13. What are polar satellites?
Q14. What are geostationary satellites?
Q15. Hydrogen is in abundance around the Sun but not around the earth. Explain.
Q16. Why the space rockets are generally launched from west to east.
Q1. State Kepler's laws of planetary motion
Q2. Derive the relation between acceleration due to gravity 'g' at the surface of a planet and Gravitational constant (G).
Q3. How does acceleration due to gravity 'g' change with height(h) and depth (d)?
Q4. What is Orbital speed? Obtain an expression for it.
Q5. What is Escape speed? Obtain an expression for it.
Q6. What is a geostationary satellite? State its uses.
Q7. What is a polar satellite? State its uses.
Q8. Write any four differences between geostationary and polar satellites.
Q9. Calculate the value of acceleration due to gravity at a height \(500\,\mathrm{km}\) above the surface of earth and at a depth of \(1000\,\mathrm{km}\) inside earth.
Q10. If a nut becomes loose and gets detached from a satellite revolving around the earth, will it fall down to earth or will it revolve around earth? Justify your answer.
Q11. The weight of an object is greater at poles than at equator. At which of these places do we get more sugar for the same weight? Explain.
Q12. If it is safe to jump from a height of \(2\,\mathrm{m}\) on earth, then calculate the safe height on planet having \(g=1.96\,\mathrm{m\,s^{-2}}\).
Q13. Is it correct to say that we are living at the bottom of a gravitational well. Justify your answer.
Q14. Prove that if two spheres of same material, mass and radius are put in contact with each other, then the gravitational attraction between them is directly proportional to the fourth power of their radius.
Q15. Define escape and orbital speeds. Find the ratio of escape speed to orbital speed.
Q16. Derive the equation for the time period of a satellite orbiting around very close to the surface of the earth.
Q1. State Newton's universal law of Gravitation. Explain how the value of gravitational constant (G) can be determined by Cavendish method.
Q2. Define gravitational potential energy and derive an expression for it associated with two particles of masses \(m_1\) and \(m_2\).
Q3. Derive an expression for acceleration due to gravity(g) for (i) at a height h above and (ii) at a depth h below the surface of the earth.
Q1. Two spherical balls each of mass \(1\,\mathrm{kg}\) are placed \(1\,\mathrm{cm}\) apart. Find the gravitational force of attraction between them.
Q2. The mass of a ball is four times the mass of another ball. When these balls are separated by a distance of \(10\,\mathrm{cm}\), the force of gravitation between them is \(6.67\times10^{-7}\,\mathrm{N}\). Find the masses of the two balls.
Q3. Three spherical balls of masses \(1\,\mathrm{kg}\), \(2\,\mathrm{kg}\) and \(3\,\mathrm{kg}\) are placed at the corners of an equilateral triangle of side \(1\,\mathrm{m}\). Find the magnitude of gravitational force exerted by the \(2\,\mathrm{kg}\) and \(3\,\mathrm{kg}\) masses on the \(1\,\mathrm{kg}\) mass.
Q4. At a certain height above the earth's surface, the acceleration due to gravity is \(4\%\) of its value at the surface of earth. Determine the height.
Q5. A satellite is orbiting the earth at a height of \(1000\,\mathrm{km}\). Find its orbital speed.
Q6. A satellite orbits the earth at a height equal to the radius of earth. Find its (i) orbital speed and (ii) Period of revolution.
Q7. The gravitational force of attraction between two objects decreases by \(36\%\) when the distance between them is increased by \(4\,\mathrm{cm}\). Find the original distance between them.
Q8. Four identical masses of \(m\) are kept at the corners of a square of side \(a\). Find the gravitational force exerted on one of the masses by the other masses.
Q9. Two spherical balls of \(1\,\mathrm{kg}\) and \(4\,\mathrm{kg}\) are separated by a distance of \(12\,\mathrm{cm}\). Find the distance of a point from the \(1\,\mathrm{kg}\) mass at which the gravitational force on any mass becomes zero.
Q10. Three uniform spheres each of mass \(m\) and radius \(R\) are kept in such a way that each touches the other two. Find the magnitude of the gravitational force on any one of the spheres due to the other two.
Q11. Two satellites are revolving round the earth at different heights. The ratio of their orbital speeds is \(2:1\). If one of them is at a height of \(100\,\mathrm{km}\), what is the height of the other satellite?
Q12. A satellite is revolving round in a circular orbit with a speed of \(8\,\mathrm{km\,s^{-1}}\) at a height where the value of acceleration due to gravity is \(8\,\mathrm{m\,s^{-2}}\). How high is the satellite from the earth's surface? (Radius of planet = \(6000\,\mathrm{km}\))
Q13. (a) Calculate the escape velocity of a body from the earth's surface. (b) If the earth were made of wood, its mass would be \(10\%\) of its current mass. What would be the escape velocity, if the earth were made of wood?
Q1. Let the speed of the planet at the perihelion P in Fig. 8.1(a) be \(v_P\) and the Sun-planet distance SP be \(r_P\). Relate \((r_P,v_P)\) to the corresponding quantities at the aphelion \((r_A,v_A)\). Will the planet take equal times to traverse BAC and CPB?
Q2. Three equal masses of \(m\,\mathrm{kg}\) each are fixed at the vertices of an equilateral triangle ABC. (a) What is the force acting on a mass \(2m\) placed at the centroid O of the triangle? (b) What is the force if the mass at the vertex A is doubled? Take \(AO=BO=CO=1\,\mathrm{m}\).
Q3. Find the potential energy of a system of four particles placed at the vertices of a square of side \(l\). Also find the potential at the centre of the square.
Q4. Two uniform solid spheres of equal radii \(R\), but masses \(M\) and \(4M\) have a centre to centre separation \(6R\), as shown in Fig. 8.10. The two spheres are held fixed. A projectile of mass \(m\) is projected from the surface of the sphere of mass \(M\) directly towards the centre of the second sphere. Obtain an expression for the minimum speed of the projectile so that it reaches the surface of the second sphere.
Q5. The planet Mars has two moons, phobos and deimos. (i) Phobos has a period \(7\) hours, \(39\) minutes and an orbital radius of \(9.4\times10^3\,\mathrm{km}\). Calculate the mass of Mars. (ii) Assume that Earth and Mars move in circular orbits around the sun, with the Martian orbit being \(1.52\) times the orbital radius of earth. What is the length of the Martian year in days?
Q6. Weighing the Earth: You are given the following data: \(g=9.81\,\mathrm{m\,s^{-2}}\), \(R_E=6.37\times10^6\,\mathrm{m}\), the distance to the moon \(r=3.84\times10^8\,\mathrm{m}\) and the time period of the moon's revolution is \(27.3\) days. Obtain the mass of the Earth \(M_E\) in two different ways.
Q7. Express the constant \(k\) of Eq. (8.38) in days and kilometres. Given \(k=10^{-13}\,\mathrm{s^2\,m^{-3}}\). The moon is at a distance of \(3.84\times10^5\,\mathrm{km}\) from the earth. Obtain its time period of revolution in days.