Question

8(a)(i) Define a torque. (ii) State three factors that determine a torque. (b)(i) Define free fall. (ii) A body is thrown vertically upward from the top of a tower 40.0 m high with a velocity of 10.0 ms^-1. Calculate the time taken for the body to reach the ground. (g=10 ms^-2) (c) A cube of wood of side 8.0 cm, floats at the interface between oil and water with 2.0 cm of its lower surface below the interface as shown in the diagram below. Given that the relative densities of oil and water are 0.72 and 1.00 respectively. Calculate the mass of the wood.

Accepted Answer

(a)(i) A torque is defined as the turning effect of force about a pivot or an axis.
(ii) Factors that determine a torque: Perpendicular distance of the force from its line of action to the pivot; Direction of the force; Magnitude of the force.
(b)(i) A free fall is defined as the vertical motion of a body under the influence of acceleration due to gravity, or its own weight.
(ii) Given u=10m/s, height of tower=40m. Using H=ut+(1/2)gt^2, taking downward as positive from the top of the tower and the body thrown upward first: -40=10t-(1/2)(10)t^2. -40=10t-5t^2. 5t^2-10t-40=0. Divide through by 5: t^2-2t-8=0. t^2-4t+2t-8=0. t(t-4)+2(t-4)=0. (t+2)(t-4)=0. t=-2 or t=4. Since time cannot be negative, t=4 s.
(c) Given: Mass of wood = mass of water displaced + mass of oil displaced. Mass of wood = (rho.V)oil + (rho.V)water, where rho_oil = density of oil = 0.72x1000=720 gcm^-3(kg/m3 equivalent), rho_water = density of water = 1x1000=1000 gcm^-3. With V_oil = volume of oil displaced = volume of portion of wood in oil = lbh = 8x8x6cm^3=384cm^3=384x10^-6 m^3. Similarly, V_water = volume of water displaced = volume of portion of wood inside water = lbh(l=b=8cm, h=2cm)=128cm^3=128x10^-6 m^3. Thus, mass of wood = [720x384+1000x128]x10^-6 = [276,480+128,000]x10^-6 = [404,480]x10^-6 = 0.404 kg.

WAEC Physics 2020 Theory — Question 8

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