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(a) Prove that the moment of inertia of a uniform rod, of mass m and length 2l, about an axis through its centre, perpendicular to its plane, is 1/2 ml^2. (b) A uniform rod, of length one metre and with centre O, oscillates about a horizontal axis throu
(2015)
(a) A hollow spherical copper ball just floats in water completely immersed. (b) A ship, of mass 6500 tonnes, is observed to sink 0.375 m in sea-water when loaded with M tonnes of cargo.
(a) Two cars, A and B, start from rest at O and begin to travel in the same direction. (b) A company uses a cost function C(x) to estimate the cost of producing x items. The cost function is given by the equation C(x)=F+V(x) where F is the estimate of a
(a) A car has an initial speed of u m s–1. It moves in a straight line with constant acceleration f for 4 seconds. (b) A particle is projected vertically upwards with a velocity of u m s–1.
(2016)
(a) At 12 noon, ship A is north west of ship B as shown. (b) A man can swim at 5/6 m s–1 in still water. He swims across a river 125 m wide.