If a planet was suddenly stopped in its orbit, supposed circular, show that it will fall into the sun in a time which is times the period of the planet’s revolution.
To solve this numerically, let's first analyze the situation where a planet is suddenly stopped in its orbit, assuming it's moving in a circular orbit. The aim is to show that the time it will take for the planet to fall into the Sun is \(\frac{\sqrt{2}}{8}\) times the period of its revolution. ### Step 1: Planet’s Circular Motion before it is Stopped Let the planet be in a circular orbit around the Sun with a period \(T\) and radius \(r\). The gravitational force provides the centripetal force that keeps the planet _________ ________ _____ ____ ___ ______ __________.
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A particle moving in .H.S M has got the velocities cm8 /sec and cm6 /sec when it is at distance cm3 and cm4 respectively from the centre of its motion. Determine the period and the amplitude of motion.
A parachutist, whose weight (actually mass) is 64 kg, drops from a helicopter 5000 m. above the ground. She falls towards the earth under the influence of gravity. Assume that the gravitational force is constant. Assume that the force due to air resistance is proportional to the velocity of the parachutist. The proportionality constant is sec when the parachute is closed, and is sec
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Consider the following system of equations
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A particle of mass m moves on a straight line towards the centre of attraction, starting from rest at a distance a from the centre. Its velocity at a distance x from the centre varies as . Find the law of force.
When an aeroplane ascends from take-off to an altitude of 10 km, by how much does the gravitational attraction acting on it decrease?