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(a) Prove that the moment of inertia of a uniform rod of mass m and length 2 l about an axis through its centre perpendicular to the rod is 1/3 ml^2. (b) Three equal uniform rods, each of length 2 l and mass m, form the sides of an equilateral triangle
(2009)
(a) A uniform cylindrical piece of wood 12 cm long floats in water with its axis vertical and 10 cm of its length immersed. (b) A thin uniform rod pq of weight W is in equilibrium in an inclined position with end p immersed in a container of water.
(a) Solve the differential equation dy/dx=1/xy+y/x given that y =√ 3 when x =1. (b) A particle of mass m is projected vertically upwards with speed u. The air resistance is 2 kv per unit mass when the speed is v.
(a) A car is travelling at a uniform speed of 14 1 m/s when the driver notices a traffic light turning red 98 m ahead. (b) A particle passes P with speed 20 m/s and moves in a straight line to Q with uniform acceleration.
(2010)
(a) Two particles, A and B, start initially from points with position vectors 6i-14j and 2i-3j respectively. (b) When a motor-cyclist travels along a straight road from South to North at a constant speed of 12.5 m/s the wind appears to her to come from a
