A solid cone hangs from a frictionless pivot at the origin O, as shown. If î, ĵ and k̂ are unit vectors, and a, b, and c are positive constants, which of the following forces F applied to the rim of the cone at a point P results in a torque τ on the cone with a negative component τz?

Question

G1 Physics · Accepted Answer

The z-component of torque is τ(z)=rₓFᵧ-rᵧFₓ. For option C, rₓ=-b and Fᵧ=a, so τ(z)=-ab<0. Options A and B have Fₓ=Fᵧ=0, so τ(z)=0. Therefore option C.