A triangular plate is shown. A force F⃗ = 4î - 3ĵ is applied at point P. The torque at point P with respect to point 'O' and 'Q' are :

Solution

Physics sir · 4 steps

Find P's position from each pivot, then take r⃗ × F⃗ in that order, and watch the signs.

1. Locate the points. The triangle is equilateral with side 10 cm. With O at the origin, Q is at (10, 0) and P is at (10 cos 60°, 10 sin 60°) = (5, 5√3), all in cm.

   τ⃗ = r⃗ × F⃗ = (xF_y - yFₓ)k̂

2. About O. r⃗_(OP) = 5î + 5√3 ĵ and F⃗ = 4î - 3ĵ. So τ_O = (5)(-3) - (5√3)(4) = -15 - 20√3, along k̂.
3. About Q. r⃗_(QP) = r⃗_P - r⃗_Q = -5î + 5√3 ĵ. So τ_Q = (-5)(-3) - (5√3)(4) = 15 - 20√3, along k̂.
4. So. The torques about O and Q are -15 - 20√3 and 15 - 20√3 (in N cm), which is option (d).

The idea to keep. Torque about a point uses the vector from that point to where the force acts, r⃗ = r⃗_P - r⃗ₚᵢᵥₒₜ, and the order is always r⃗ × F⃗. Reverse it and every sign flips.

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