A block is suspended in equilibrium by two light strings attached to a horizontal ceiling. The first string makes an angle of 45^ with the ceiling. If the tension in the second string is 2 times the tension in the first string, the angle made by the second string with the ceiling is :

Step-by-step solution

Let the tension in the first string be T₁ and the tension in the second string be T₂ . The first string makes an angle of 45^ with the horizontal ceiling, and the second string makes an unknown angle with the ceiling. For the block to be in horizontal equilibrium, the horizontal components of the tensions in the two strings must be equal and opposite. T₁ (45^ ) = T₂ ( ) It is given that T₂ = 2 T₁ . Substituting this into the equilibrium equation gives: T₁ ( 1 2 ) = ( 2 T₁) ( ) Dividing both sides by T₁ (since T₁ 0