Question Number 465 by shubham last updated on 09/Jan/15
$${A}\:{particle}\:{moves}\:{with}\:{a}\:{central}\:{acceration}\:{varies}\:{as}\:{the}\:{cube}\:{of}\:{the}\:{distance}.\:{if}\:{it}\:{be}\:{projected}\:{from}\:{an}\:{apse}\:{at}\:{distance}\:{a}\:{from}\:{the}\:{origin}\:{with}\:{a}\:{velocity}\:{which}\:{is}\:\sqrt{\mathrm{2}\:}\:{times}\:{the}\:{velocity}\:{for}\:{a}\:{circle}\:{of}\:{radius}\:{a}.\:{show}\:{that}\:{the}\:{equation}\:{of}\:{path}\:{is}\:{its}\:{r}\mathrm{cos}\theta/\sqrt{\mathrm{2}}\:=\:{a} \\ $$
Commented by prakash jain last updated on 09/Jan/15
$$\mathrm{Reformatted} \\ $$$${A}\:{particle}\:{moves}\:{with}\:{a}\:{central} \\ $$$${acceration}\:{varies}\:{as}\:{the}\:{cube}\: \\ $$$${of}\:{the}\:{distance}.\:{if}\:{it}\:{be}\:{projected} \\ $$$${from}\:{an}\:{apse}\:{at}\:{distance}\:{a} \\ $$$${from}\:{the}\:{origin}\:{with}\:{a}\:{velocity} \\ $$$${which}\:{is}\:\sqrt{\mathrm{2}\:}\:{times}\:{the}\:{velocity} \\ $$$${for}\:{a}\:{circle}\:{of}\:{radius}\:{a}.\:{show}\:{that} \\ $$$${the}\:{equation}\:{of}\:{path}\:{is} \\ $$$${its}\:{r}\mathrm{cos}\theta/\sqrt{\mathrm{2}}\:=\:{a} \\ $$