Questions in statics

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A body consists of a solid cylinder with radius a and height a together with a solid hemisphere of radius a placed on the base of the cylinder. The centre of gravity of the complete body is
The centre of gravity G of three particles of equal mass placed at the three vertices of a right angled isosceles triangle whose hypotenuse is equal to 8 cm is on the median through A such that AG is
Weights 2, 3, 4 and 5 lbs are suspended from a uniform lever 6 ft long at distances of 1, 2, 3 and 4 ft from one end. If the weight of the lever is 11 lbs, then the distance of the point at which it will balance from this end is
On the same base AB, and on opposite side of it, isosceles triangles CAB and DAB are described whose altitudes are 12 cm and 6 cm respectively. The distance of the centre of gravity of the quadrilateral CADB from AB, is
In a triangle ABC right angled at C, the lengths of sides AC and BC are 3 cm and 4 cm respectively. Parallel forces each equal to P act at the vertices A,B,C and parallel forces each equal to 2P act at the middle points of all the sides of the triangle. The distance of C.G. from the vertex C is

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