A Unifrom 263 n rod that is 187 m long caries a n weght at i

A Unifrom 263 n rod that is 1.87 m long caries a n weght at its right end an towerd the left end (see the figure) when w is plased cm from the left of the rod the system just balances.

Solution

the length of the rod is 187cm

weight is 263 N

the fulcum is located at 70.6 cm from the right

weight of the rod per unit length is, w=263/187 N/cm

weight of the right side is w*70.6 N=99.3N

weight of left side is 163.7N

For the the center of mass is located at 35.3cm for the right side and 58.2 cm for the left side .

So now to calculate W, equating the torque o both side.

35.3*99.3+70.6*225=58.2*163.7+(187-70.6-57.1)*W

so, W=166.3N