A particle of mass m is projected from point A with an initial velocity V0 perpendicular to line OA and moves under a central force F along a semicircular path of diameter OA. Observing that r0cos θ=r and using mr2dθ/dt=angular momentum, show that the speed of the particle is v=v0/cos2θ.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.