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A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle θ to the horizontal, the maximum height attained by it is 4R. The angle of projection, θ is then given by :
Asked by roshnibhati921 | 03 Nov, 2023, 01:15: PM
answered-by-expert Expert Answer
If the particle is moving with uniform speed in a circle of radius R 
and it takes time T to complete one revolution ,then uniform speed u is
 
begin mathsize 14px style u space equals space fraction numerator 2 straight pi straight R over denominator T end fraction end style ................................... (1)
 
If the particle is projected with speed u at angle θ , then maximum height H reached
by particle is
 
begin mathsize 14px style H space equals space fraction numerator u squared sin squared theta over denominator 2 g end fraction end style ............................(2)
By substituting H = 4R , and  velocitiy u from eqn.(1) , we get
 
begin mathsize 14px style 4 R space equals space fraction numerator 4 straight pi squared straight R squared space cross times space sin squared straight theta over denominator T squared space cross times space left parenthesis 2 g right parenthesis end fraction space end style
 
From above expression , we get
 
begin mathsize 14px style sin theta space equals space T over pi square root of fraction numerator 2 g over denominator R end fraction end root end style

Answered by Thiyagarajan K | 03 Nov, 2023, 02:35: PM
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A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle θ to the horizontal, the maximum height attained by it is 4R. The angle of projection, θ is then given by :
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