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An object is made by hanging a ball of mass $M$ from one end of a plank having the same mass and length $L$. The object is then pivoted at a point a distance $L/4$ from the end of the plank supporting the ball, as shown.

I would like to know why the above is true. Since $\tau= \mid r \mid \mid F \mid \sin \theta$, given that $\sin \theta$ is when $\theta=90^{\circ}$. The torque should then be $\tau= rF$ when assuming the axis to be a standard xy-plane. Am I supposed to figure out how $F_g= \tau$ where the some of the variables cancel? I don't really see it. How should I approach this problem to gain further understanding?

thanks in advance!

  • $\begingroup$ This should be pretty straight forward. Don't overcomplicate it. As @M_ points out the weight of the plank (M) can be assumed located at its midpoint, which is another 1/4 L to the right of the pivot point. From there it should be obvious that the planck is balanced. $\endgroup$ – Bob D Nov 15 '18 at 17:40

Please note that the rod is not massless. The gravitational force can be effectively applied to the centre of gravity.

Hope this gives you some direction.

Some additional hint: center of gravity of an uniform rod is located at its midpoint. Thus the opposing torque could come from the weight of the rod itself.


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