A force -P k̂ acts at the origin. The torque about the point (2, -3) is P(aî + bĵ). If a/b = x/2, find x.

Question

G1 Physics · Accepted Answer

Position vector from the point (2, -3) to the origin is r = -2î + 3ĵ Force: F = -P k̂ Torque: τ = r × F = (-2î + 3ĵ) × (-P k̂) Using î × k̂ = -ĵ and ĵ × k̂ = î, τ = -3Pî - 2Pĵ = P(aî + bĵ) Thus, a = -3 b = -2 Therefore, a/b = 3/2 Given a/b = x/2: x = 3 Final value: 3