A force of -P k̂ acts on the origin of the coordinate system. The torque about the point (2,-3) is P(a î+b ĵ), The ratio of a/b is x/2. The value of x is -

Solution

Physics sir · 3 steps

Draw the vector from the pivot to the point where the force acts, then cross it with the force.

1. Position vector. Torque about a point uses r⃗ drawn from that point to where the force acts. Here the pivot is (2,-3,0) and the force acts at the origin, so r⃗ = (0-2)î + (0+3)ĵ = -2î + 3ĵ.

   τ⃗ = r⃗ × F⃗ = |î, ĵ, k̂; -2, 3, 0; 0, 0, -P|

2. Expand. The î term is 3(-P) - 0 = -3P. The ĵ term is -[(-2)(-P) - 0] = -2P. The k̂ term is 0. So τ⃗ = P(-3î - 2ĵ).
3. So. a = -3 and b = -2, so a/b = 3/2 = x/2, which gives x = 3.

The common slip: -3. Forgetting the minus sign in front of the ĵ term makes b = +2, so a/b = -3/2 and x = -3.

The idea to keep. Torque about any point is r⃗ × F⃗, with r⃗ running from that point to where the force acts. Watch the minus sign on the ĵ term of the determinant.

Answer from the NTA final answer key. Solution by PrepWiser.