A stone of mass 2 ~kg is hung from the ceiling of the room using two strings. If the strings make an angle 60^ and 30^ respectively with the horizontal surface of the roof then the tension on the longer string is : g=10 ~ms ⁻²

Step-by-step solution

The string making 30° with the horizontal is longer. Let T₁ and T₂ be tensions in strings at 60° and 30° respectively. Weight W = mg = 20 N. Horizontal equilibrium: T₁ 60° = T₂ 30° T₁ 1 2 = T₂ 3 2 T₁ = 3 T₂ Vertical equilibrium: T₁ 60° + T₂ 30° = 20 Substituting T₁ = 3 T₂ : 3 T₂ 3 2 + T₂ 1 2 = 20 T₂ ( 3 2 + 1 2 ) = 20 2T₂ = 20 T₂ = 10 N