Torque - Practice Questions & MCQ

• Vector product of Force vector and position vector is known as torque.

• - $\vec{\tau}=\underset{r}{\rightarrow} \times \underset{F}{\vec{F}}$
  - Its direction is always perpendicular to the plane containing vector r and F and with the help of right hand screw rule we can find it.
  - The magnitude of torque is calculated by using either
  - $\tau=r_1 F$ or $\tau=r \cdot F_1$
  $r_1=$ perpendicular distance from origin to the line of force.
  $F_1=$ component of force perpendicular to line joining force.
  - $\tau=r . F \cdot \sin \phi$

  Where $\phi_{\text {is the angle between vector } r \text { and } \mathrm{F}}$
  - $\tau_{\text {max }}=r . F\left(\right.$ when $\left.\phi=90^{\circ}\right)$
  - $\tau_{\min }=0\left(\right.$ when $\left.\phi=0^0\right)$

•  If a pivoted, hinged  body tends to rotate due to an applied force, then it is said  that torque is acted on body by force.

Example-

In the rotation of a hinged door when we apply torque with the help of force F.
- SI Unit- Newton-metre
- Dimension- $M L^2 T^{-2}$
- If a body is acted upon by more than one force, then we get the resultant torque by doing vector sum of each torque.

$
\tau=\tau_1+\tau_2+\tau_3 \ldots \ldots
$

- Just like force is the cause of translatory motion similarly Torque is the cause of rotatory motion.