A small block of mass m (= 1 kg) is pulled on a frictionless horizontal surface by means of a light rope at a rate of u ( = 10 m / s ) with a pulley situated at a height h ( = 9 m ) above the level of

Question

A small block of mass m (= 1 kg) is pulled on a frictionless horizontal surface by means of a light rope at a rate of u ( = 10 m / s ) with a pulley situated at a height h ( = 9 m ) above the level of block. The block was initially placed at a very large distance from the pulley. Find the angle θ (in degree) of rope with horizontal, when the block leaves the surface.

TestHub · Accepted Answer

Constraint motion: v = u sec θ , so a = u sec θ tan θ d t d θ ​ From x = h cot θ : v = h csc 2 θ d t d θ ​ When the block leaves the surface, N = 0 : T sin θ = m g , T cos θ = ma , so a = g cot θ Eliminating d t d θ ​ between the relations: tan 2 θ = u g h ​ ​ = 9 ​ = 3 tan θ = 3 ​ , so θ = 6 0 ∘

Physics - NLM Question with Solution | TestHub

Doubts & Discussion