Question
A hollow vertical cylinder of radius R and height h has smooth internal surface. A small particle is placed in contact with the inner side of the upper rim at a point P. It is given a horizontal speed vo tangential to rim. It leaves the lower rim at point Q, vertically below P. The number of revolutions made by the particle will
Answer: Option D
:
D
since the body has no initial velocity in the vertical direction.
az=-g, vertical displacement z=-h.
∴z=at+12at2
⇒−h=0+12(−g)t2
⇒T=√2hg time taken to reach the bottom
let,t be the time taken to complete one revolution.
Then t=2πRv0
∴ number of revolution=Tt=√2hg2πRv0=v02πR√2hg
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:
D
since the body has no initial velocity in the vertical direction.
az=-g, vertical displacement z=-h.
∴z=at+12at2
⇒−h=0+12(−g)t2
⇒T=√2hg time taken to reach the bottom
let,t be the time taken to complete one revolution.
Then t=2πRv0
∴ number of revolution=Tt=√2hg2πRv0=v02πR√2hg
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