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Standard X

Physics

Free Fall

a body of mas...

Question

a body of mass 'm' is dropped from a distance r from the centre of earth of mass M and radius R. WIth what speed the body strikes the surface of the earth? neglecting air resistance.

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Solution

$A c c e l e r a t i o n d u e t o g r a v i t y o n t h e s u r f a c e o f t h e e a r t h . g = \frac{G M}{R^{2}} l e t t i s t h e t i m e t a k e n t o t r a v e l t h e d i s \tan c e r r = u t + \frac{1}{2} g t^{2} A s b o d y i s d r o p p e d, i n i t i a l v e l o c i t y u = 0 r = \frac{1}{2} g t^{2} t = \sqrt{\frac{2 r}{g}} f i n a l v e l o c i t y w i t h w h i c h b o d y r e a c h t o t h e s u r f a c e o f t h e e a r t h . v = u + g t v = 0 + g t v = g \sqrt{\frac{2 r}{g}} v = \sqrt{2 r g} v = \sqrt{\frac{2 r G M}{R^{2}}} w h e r e G i s t h e g r a v i t a t i o n a l c o n s \tan t .$

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