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Grade: 11

                        

An isosceles triangle is to be cut from one edge of a square lamina such that the remaining portion when suspended from the apex P of the cut will remain in equilibrium in any position. The value of h is A: (3-3^1/2)l/2 B: (3+3^1/2)l/2 C: (2-2^1/2)l/2 D: (2+2^1/2)l/2

2 years ago

Answers : (1)

Arun
24738 Points
							
Let M be the mass of square.Mass per unit area=M÷(l×l).Mass of isosceles triangle=M÷(l×l)×(1÷2×l×h).Set origin at apex P.y of com =0=M×(l÷2-h)-M÷(l×l)×(1÷2×l×h)×(-2÷3×h).On solving the quadratic equation obtained,h=(3+or-root 3)÷2Since h cannot be >l.Thus h=(3-root 3)÷2.
2 years ago
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