A horizontal, nonuniform beam of mass M and length L is hinged to a vertical wal

Question

A horizontal, nonuniform beam of mass M and length L is hinged to a vertical wall at one side, and attached to a wire on the other end. The wire exerts a force T at an angle of with respect to the vertical. If the mass of the beam is 10 kg, the tension in the wire is 50 N, sin(theta)=3/5 and cos(theta)=4/5, how far is the center of mass of the beam from the hinge? The acceleration due to gravity is 10 m/s2.
1. 0.3L
2. 0.375L
3. 0.16L
4. 0.625L
5. 0.32L
6. Not enough information is given.
7. 0.4L
8. 0.666667L
9. 0.5L, of course
10. 0.18L

Explanation / Answer

let us assume the orizen at fixed end of the beam

F1=10*10=100N

r1=x

F2=50N

r2=L                 cos=4/5 as is with the vertical

now applying =0

F1r1+F2r2=0

100*x=50*L*4/5

x=0.4Lm from the fixed eend

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