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