(a)i) Define a torque. (ii)State three factors that determine a torque (b)(i) Define free fall. (ii) A body is thrown vertically upwards from the top of a t...

(a)(i) The torque (moment) of a force about a point is the turning effect of the force about that point; it is the product of the force and the perpendicular distance of its line of action from the point (the axis of rotation): \(\tau=F\times d\).

(a)(ii) Factors that determine a torque:

• The magnitude of the applied force.
• The perpendicular distance between the line of action of the force and the pivot (axis).
• The angle at which the force is applied relative to the arm (line of action direction).

(b)(i) Free fall is the motion of a body falling only under the action of gravity, with no other force (such as air resistance) acting on it; its acceleration is g.

(b)(ii) Take upward positive, u = 10.0 m/s, tower height 40.0 m so displacement to the ground = -40.0 m, g = 10.0 m/s\(^2\).

\[s=ut-\tfrac{1}{2}gt^{2}\Rightarrow-40=10t-5t^{2}.\]

\[5t^{2}-10t-40=0\Rightarrow t^{2}-2t-8=0\Rightarrow(t-4)(t+2)=0.\]

Taking the positive root, \(t=4\,\text{s}\).

(c) Cube side 8.0 cm, so face area \(A=8\times8=64\,\text{cm}^2\). It floats with 2.0 cm below the oil-water interface (in water) and \(8-2=6\,\text{cm}\) in the oil. By the principle of flotation, the weight of the wood equals the total upthrust from oil and water.

Mass \(=\rho_{water}V_{water}+\rho_{oil}V_{oil}\) (using densities in g/cm\(^3\): water 1.00, oil 0.72).

\(V_{water}=64\times2=128\,\text{cm}^3\); \(V_{oil}=64\times6=384\,\text{cm}^3\).

\[m=(1.00\times128)+(0.72\times384)=128+276.48=404.48\,\text{g}\approx404.5\,\text{g}.\]