Earth rotates around the Sun with time period = TDue to some cosmic event the earth's rotation and revolution,Sun pulls Earth toward its center i)Find the velocity v when it's distance is x from sun's center ii)Find the Time taken to reach the velocity v and The time taken to reach the sun's center.

1
by Souvik118
There is a clarification. In the 2nd line two words are missing. It should read:
... Earth's rotation and revolution stops and the Sun pulls Earth ...
yes

2014-10-19T17:43:06+05:30

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As the Earth is revolving around the Sun under the influence of a centripetal acceleration "a", with an angular velocity "ω" at a time period T.  Let the radius of Earth's orbit be R, Ms be the mass of Sun and the mass of Earth be Me. Let G be the universal Gravitational constant.Centripetal force is supplied by the gravitational attraction force. Hence,

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Let us assume that the gravitational force of attraction on the Earth pulls it towards the Sun and the Earth starts from an initial velocity 0 at t=0.  Let us assume that Earth starts from rest. (no rotational or other kinetic energy).

Force on the Earth at a distance R from the Sun = Fg = G Ms Me / R²
Work done by F for moving Earth to a distance x from R = Wg =

Kinetic energy gained by Earth = Change in gravitational PE = Wg

Where x₀ = R = distance of Earth from Sun at t = 0.

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To derive expression for t in terms of x and v.

So time to reach the Sun is T/4
√2
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Time duration for Earth to reach velocity v.

It takes a long time...
yeah i know the question was too tough
thank you
difficulty is not due to the toughness. it is due to complicated and long expressions.
yeah and i have not learnt integration till now so i was having a problem