Question

Three forces acting on a body are shown in the figure to have resultant force only along the y direction the magnitude of minimum additional force needed is

Answer 1

first of all, write the component of all forces.
for force of 4N,
x - component => 4sin30° = 2N(←)
y - component => 4cos30° = 2√3N(↑)

for force of 2N,
x - component => 2cos60° = 1N(→)
y - component => 2sin60° = √3N(↓)

for force of 1N,
x - component => 1cos60° = 0.5N(→)
y - component => 1sin60° = 0.5√3N(↑)

A/c to question,
resultant force only along Y direction, so net force along x direction must be zero.
e.g., force along x direction (→) = force along x direction (←)
1N + 0.5 N ≠ 2N
so, we have to add minimum 0.5 N force forward direction


now, you can see in y- direction,
net force along y direction ≠ 0

hence, answer is option (3)

Answer 2

Please refer the attachment.

The answer should be 3) 0.5 N