# Force F = (9.0 N)i + (-7.0 N)k acts on a pebble with position vector r = (0.40 m)j + (-2.4 m)k,...

## Question:

Force {eq}F = (9.0 N)i + (-7.0 N)k {/eq} acts on a pebble with position vector {eq}r = (0.40 m)j + (-2.4 m)k {/eq}, relative to the origin.

a. What is the resulting torque acting on the pebble about the origin?

b. What is the resulting torque acting on the pebble about a point with coordinates (8.0 m, -6.0 m, -5.0 m)?

## Torque

The torque due to a force about origin is given by-

{eq}\vec{\tau}\ =\ \vec{f}\times \vec{r}\\ {/eq}

Where,

• {eq}\tau \ =\ {/eq}torque.
• {eq}\vec{f}\ =\ {/eq}force
• {eq}\vec{r}\ =\ {/eq}position vector.

Given:-

• {eq}\vec{f}\ =\ (9.0\ N)\hat{i}+(-7.0\ N)\hat{k}. {/eq}
• {eq}\vec{r}\ =\ (0.40\ m)\hat{i}+(-2.4\ m)\hat{k}. {/eq}

Part-a:-

The torque due to a force about origin is given by-

{eq}\vec{\tau}\ =\ \vec{f}\times \vec{r}\ =\ ((9.0\ N)\hat{i}+(-7.0\ N)\hat{k})\times ((0.40\ m)\hat{i}+(-2.4\ m)\hat{k})\ =\ (21.6)\hat{j}-(2.8)\hat{j}\ =\ 18.8\hat{j}\\ {/eq}

Part-b:-

Given:-

• {eq}\vec{r}\ =\ (-54)\hat{i}-(6.0)\hat{j}-.(5.0)\hat{k}. {/eq}

The torque due to a force about origin is given by-

{eq}\vec{\tau}\ =\ \vec{f}\times \vec{r}\ =\ ((9.0\ N)\hat{i}+(-7.0\ N)\hat{k})\times ((-54)\hat{i}-(6.0)\hat{j}-(5.0)\hat{k})\ =\ (42)\hat{i}-(11)\hat{j}-((54)\hat{k}\\ {/eq}