Taking the unit vectors
i and
j as upwards and to the right, the forces acting are:
- a weight force of W = -mgj
- the tension in the string of T = +Fj
- the friction force of
- the normal force of
The sum of these forces is
Since the object is stationary, this sum must be the zero vector. It then follows, from the
i components, that:
and, from the
j components, that:
and the answer is (D).
Note, substituting the value 37 degrees gives
F = 0.375708...
mg, which is far closer to (D) than to any of the other options.