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How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is `1.5 × 10^8`
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A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is `1.50 × 10^8` km away from the sun
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A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth
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Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface
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A rocket is fired vertically with a speed of 5 km `s^(-1)` from the earth’s surface. How far from the earth does the rocket go before returning to the earth ? Mass of the earth = `6.0 × 10^(24)` kg; mean radius of the earth = `6.4 × 10^6`m; G = `6.67 × 10^(–11)` N `m^2`
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The escape speed of a projectile on the earth’s surface is 11.2 km `s^(-1)`. A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other
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A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite = 200 kg; mass of the earth = 6.0×1024 kg; radius of the earth = `6.4 × 10^6` m; G = `6.67 × 10^(–11)` N `m^2`
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Two stars each of one solar mass (= `2×10^(30)` kg) are approaching each other for a head on collision. When they are a distance 109 km, their speeds are negligible. What is the speed with which they collide ? The radius of each star is `10^4` km. Assume the stars to remain undistorted until they collide. (Use the known value of
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Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a horizontal table. What is the gravitational force and potential at the mid point of the line joining the centres of the spheres ? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable
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As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly 36,000 km from the surface of the earth. What is the potential due to earth’s gravity at the site of this satellite ? (Take the potential energy at infinity to be zero). Mass of the earth = `6.0×10^(24)` kg, radius = 6400
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A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity ? (mass of the sun = `2×10^(30)`
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A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system ? Mass of the space ship = 1000 kg; mass of the sun = `2×10^(30)` kg; mass of mars = `6.4×10^(23)` kg; radius of mars = 3395 km; radius of the orbit of mars = `2.28 ×10^8` km; G = `6.67 × 10^(–11)` N `m^2`
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A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s–1. If 20% of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it ? Mass of mars = `6.4×10^(23)` kg; radius of mars = 3395 km; G = G = `6.67 × 10^(–11)` N `m^2`
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What is the moment of inertia of a disc about one of its
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What is the moment of inertia of a rod of mass M, length l about an axis perpendicular to it through one
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What is the moment of inertia of a ring about a tangent to the circle of the
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Find the centre of mass of three particles at the vertices of an equilateral triangle. The masses of the particles are 100g, 150g, and 200g respectively. Each side of the equilateral triangle is 0.5m
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Find the centre of mass of a triangular
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Find the centre of mass of a uniform L-shaped lamina (a thin flat plate) with dimensions as shown. The mass of the lamina is 3
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Find the scalar and vector products of two vectors. `a=(3hati-4hatj+5hat)` and
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