A block is placed on a horizontal surface. When a force F is applied to push the block at an angle of 30^ with the horizontal, the normal reaction from the surface is 150 N . When the same force F is applied to pull the block at the same angle of 30^ with the horizontal, the normal reaction becomes 90 N . The mass of the block is (Given g = 10 m s ⁻² )

Step-by-step solution

When the block is pushed, the vertical component of the force acts downwards. For vertical equilibrium: N₁ = mg + F 30^ = 150 When the block is pulled, the vertical component of the force acts upwards. For vertical equilibrium: N₂ = mg - F 30^ = 90 Adding the two equations, we get: N₁ + N₂ = 2mg 150 + 90 = 2mg 240 = 2m(10) 20m = 240 m = 12 kg Answer: 12 kg