A particle moves with a central acceration varies as the cube of the distance. if it be projected from an apse at distance a from the origin with a velocity which is (√(2 )) times the velocity for a circle of radius a. show that the equation of path is its rcosθ/(√2) = a


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Question Number 465 by shubham last updated on 09/Jan/15

$A p a r t i c l e m o v e s w i t h a c e n t r a l a c c e r a t i o n v a r i e s a s t h e c u b e o f t h e d i s t a n c e . i f i t b e p r o j e c t e d f r o m a n a p s e a t d i s t a n c e a f r o m t h e o r i g i n w i t h a v e l o c i t y w h i c h i s \sqrt{2} t i m e s t h e v e l o c i t y f o r a c i r c l e o f r a d i u s a . s h o w t h a t t h e e q u a t i o n o f p a t h i s i t s r \cos θ / \sqrt{2} = a$
Commented by prakash jain last updated on 09/Jan/15

$Reformatted$ $A p a r t i c l e m o v e s w i t h a c e n t r a l$ $a c c e r a t i o n v a r i e s a s t h e c u b e$ $o f t h e d i s t a n c e . i f i t b e p r o j e c t e d$ $f r o m a n a p s e a t d i s t a n c e a$ $f r o m t h e o r i g i n w i t h a v e l o c i t y$ $w h i c h i s \sqrt{2} t i m e s t h e v e l o c i t y$ $f o r a c i r c l e o f r a d i u s a . s h o w t h a t$ $t h e e q u a t i o n o f p a t h i s$ $i t s r \cos θ / \sqrt{2} = a$
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