Question

Three person p q and R pull and object with equal forces as shown in figure identify the direction of motion of the object

Answer 1

Answer:

(3)  The vertically upward  direction

Explanation:

Since:

Forces R , Q are anti parallel or making a angle of 180° that is their are in

opposite directions and also the magnitudes of all forces are equal equal.So

Therefore

Q = -R

Now

Resultant of all Forces = P + Q + R

Resultant of all Forces = P + Q - Q = P

Resultant of all Forces = P

Since

Force P is in vertically upward direction

Therefore

The Resultant will also in vertically upward direction

So

The body will move in vertically upward direction.

Answer 2

Answer:

Option (3): In vertically upwards direction.

Explanation:

Given that all the three forces are of equal magnitudes.

Let the magnitudes of all three forces be $\rm F$, such that,

$\rm |\vec P |=|\vec Q |=|\vec R |=F$.

The resultant of two vectors $\vec A$ and $\vec B$ is given by

$\text{Resultant} = \sqrt{A^2+B^2+2AB\cos\theta$.

where,

• $A,\ B$ = magnitudes of vectors $\vec A$ and $\vec B$.

• $\theta$ = angle between vectors $\vec A$ and $\vec B$.

The angle between forces $\vec Q$ and $\vec R$ is $180^\circ$.

Therefore, the resultant of forces $\vec Q$ and $\vec R$ is given by

$\text{Resultant of forces Q and R} = \sqrt{|\vec Q|^2+\vec R|^2+2|\vec Q||\vec R|\cos 180^\circ}\\= \sqrt{F^2+F^2+2F^2\cos 180^\circ}\\= \sqrt{F^2+F^2-2F^2}\\=0.$

Therefore, the two forces $\vec Q$ and $\vec R$ cancel out with each other so the net force will be along the direction of third force $\vec P$ i.e., vertically upwards direction.

Thus, option (3) is correct.