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    1)A uniform rod AB of length 4m and mass 4kg is freelg hinged at A to a vertical wall. A force P is applied at B at right angles to the rod to keep the rod in equilibrium at an angle 30 degrees to horizontal.

    Find magnitude of P and magnitude of R, the reaction at hinge.

    2) a semi-circular metal plate of radius 1m is freely hinged at A so that it can move in the vertical plane. The plate is of mass 5kg and maintained in equilibrium with boundary diameter AB vertical and B above A, by a horizontal cable attached at B and in the vertical plane of plate. By modelling the plate as uniform semiciruclar lamina, find

    Tension T in cable
    The horizontal and vertical components of the force exerted by hinge on the plate.

    3) A uniform rod AB of mass M and length 2a with the end B in contact with a rought vertical wall is held in equilibrium by a light inextensible string of length a with one end attached to the midpoint G of the rod abd the other attached to point C of the wall vertically above B. The string and rod each make an acute angle (i.e. ceta) with the horizontal.

    Show that mu, the coefficient of friction between wall and rod satisfies, mu is greater than or equal to tan ceta.

    When a force of magnitude 1/2Mg acts at A, in the direction from A to C, the sytem remains in equilibrium.

    Find in terms of M,g and ceta, expressions for horizontal and vertical components of force acting on the rod at B.

    Given mu = 0.75 deduce that tan ceta is less than or equal to 1/2.
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    Q1:

    moments about A:
    4g N * 2m * cos 30 = 4m * P N (equlibrium)

    And for the reaction at the hinge, resolve horizontally.
 
 
 
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