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(a) Prove that the moment of inertia of a uniform circular disc, of mass m and radius r, about an axis through its centre perpendicular to its plane is 1/2 mr^2. (b) Masses of 4 kg and 6 kg are suspended from the ends of a light inextensible string whic
(2008)
(a) A uniform rod, of length 2 m and relative density 7/9, is pivoted at one end p and is free to move about a horizontal axis through p. The other end of the rod is immersed in water. (b) A cylinder contains water to a height of 20 cm. A solid body o
If X^2 y (dy/dx)+y(dy/dx)=1 and y=0 when x=0, find he value of x when y=√(π/2). (b) A train of mass 200 tonnes moves along a straight level track against a resistance of 400v 2 , where v m/s is the speed of the train.
(a) A particle is projected vertically upwards from the point p. (b) A train accelerates uniformly from rest to a speed v m/s with uniform acceleration f m/s .
(2009)
(a) Two cars, A and B, travel along two straight roads which intersect at right angles. (b) The speed of an aeroplane in still air is u km/h.