Question

The two forces of 9 newtons and 12 newtons which are acting at right angles to each other will have a resultant of (a) 8 newtons (b) 10 newtons (c) 15 newtons (d) 20 newtons

Answer 1

Answer & Explanation:

Vectors are added according to the paralelogram law.  

If we arrange the vectors in a way they tails coincide, as in figure below, they will generate a rectangle, since they act at right angles to each other.

The resultant force is a vector joining the diagonal of the rectangle (see figure). The resultant vector along with the two applied forces form a right triangle, in which the forces being added are the legs(catheti) and the resultant is the hypotenuse.

The resultant is calculated from the Pythagoras theorem (the sum of the squares of the legs is equal to the square of the hypotenuse),

$F_R = \sqrt{ ( 9 \, \text{N} )^2 + ( 12 \, \text{N} )^2 } = 15 \, \text{N} \, \, .$

Answer is (c) 15 Newtons.

Answer 2

Hi mate

Here is ur answer ⬇

The resultant of two forces when they are acting perpendicular to each other is 15 N.

Explanation:

Given that,

$Force 1, F_1=9n$

$Force 2, F_2=12$

To find,

The resultant of the forces when they are perpendicular to each other.

Solution,

We know that the resultant of two forces when they are acting perpendicular to each other is given by

$F=\sqrt{9^2+12^2} \: \:$

$F= \sqrt{ 9^{2} + {12}^{2} }$

F = 15 N

So, the resultant of two forces when they are acting perpendicular to each other is 15 N.