Question

A particle is projected with a speed u at an angle θ with the horizontal. Consider a small part of its path near the highest position and take it approximately to be a circular arc. What is the radius of this circle? This radius is called radius of curvature of the curve at the point.

Answer 1

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A hemispherical bowl of radius R is rotated about its axis of symmetry which is kept vertical. A small block is kept in the bowl at a position where the radius makes an angle 0 with the vertical. The block rotates with the bowl without any slipping. The friction coefficient between the block and the bowl surface is

Answer 2

Horizontal Velocity of the Object = u Cosθ

We know that Horizontal velocity remains the same in the projectile motion throughout. Now, at the highest point Vertical velocity is zero.

∴ Resultant Velocity at highest point = ucosθ

Now,

Force of gravity = Centripetal Force

mg = mv²/r , at the higest point.

⇒ r = v²/g.

∴ r = u²cos²θ/g.  

Hope it helps.