A meter stick is found to balance at the 49.7-cm mark when placed on a fulcrum. When a 65.5-gram mass is attached at the 21.0-cm mark, the fulcrum must be moved to the 39.2-cm mark for balance. What is the mass of the meter stick

113.53 g

Explanation:

Please see attached photo for explanation.

In the attached photo, M is the mass of the meter stick.

The value of M can be obtained as shown below:

Clockwise moment = M × 10.5

Anticlockwise moment = 65.5 × 18.2

Anticlockwise moment = Clockwise moment

65.5 × 18.2 = M × 10.5

1192.1 = M × 10.5

Divide both side by 10.5

M = 1192.1 / 10.5

M = 113.53 g

Thus, the mass of the meter stick is 113.53 g

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west