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All formulas related to question of ball sliding of a smooth hemisphere from top ?(WPE)


Unknown Student 24th Mar, 2020
Answer (1)
Pratyay Islam 24th Mar, 2020

Hello Student,

I guess you wanted the formulas of when the ball or body would loose contact,what velocity etc. These are all the formulas :

Let Radius of hemisphere be R, The height of the ball from base be H .

  1. Normal Reaction on the body is zero when the ball leaves the hemisphere.
  2. Vertical height from table at which the body leaves the hemisphere is H = 2R/3
  3. If Position vector of the ball with respect to the centre of curvature makes an angle θ with the vertical when the body leaves the hemisphere, the cosθ = 2/3
  4. Velocity of block at that instant of time is V = √(2gR/3)
  5. If the block is given a horizontal velocity u from the top of smooth convex hemisphere then angle θ  with vertical at which the block leaves hemisphere is cosθ = 2/3 + u²/3gR

(g = acceleration due to gravity)

This Diagram may help


2 Comments
Comments (2)
24th Mar, 2020
Thank you very much Sir
Reply
24th Mar, 2020
Unknown Student Happy to help .
Reply

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