A small particle slides from height H = 45 cm as shown and then loops inside the vertical loop of radius R from where a section of angle θ = 6 0 ∘ has been removed. Find R (in cm) such that after losi

Question

A small particle slides from height H = 45 cm as shown and then loops inside the vertical loop of radius R from where a section of angle θ = 6 0 ∘ has been removed. Find R (in cm) such that after losing contact at A and flying through the air, the particle will reach at the point B . Neglect friction everywhere.

TestHub · Accepted Answer

COME: m g H = m g h + 2 1 ​ m v 2 with h = R + R cos 6 0 ∘ = 2 3 R ​ : 0.45 g = 2 3 R ​ g + 2 v 2 ​ ⇒ 9 − 30 R = v 2 . Projectile from A to B: horizontal 2 v ​ t = 2 R 3 ​ ​ ; vertical 2 v 3 ​ ​ t − 2 1 ​ g t 2 = 2 R ​ . Solving gives v 2 = 15 R . 9 − 30 R = 15 R ⇒ R = 45 9 ​ m = 20.00 cm

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