Question

A force of 1600 dynes acts on a rigid body, such that the perpendicular distance
between the force and its turning point is 40cm. Calculate the moment of force.
Give your answer in SI unit.

Answer 1

Answer:

$\bigstar$ Given:

⇒ Force (F) = 1600 dyne

⇒ Perpendicular distance (r) = 40 cm

$\bigstar$ To Find:

⇒ Moment of force (τ)

$\bigstar$ Solution:

⇒ Moment force = Torque (τ)

Formula to be used here is

$\boxed{ \sf {Torque = r \times F}}$

→ Since, It is a cross product

Therefore,

$\implies \sf \tau = r \;F \;sin\theta$

→ Since it is given in  the question as perpendicular

∴ θ = 90°

So,

sinθ = sin 90° = 1

Hence,

$\implies \sf \tau = r \times F$

$\implies \rm 40 \times 1600$

$\implies \rm 64000\;dyne\;cm$

$\implies \rm 64 \times 10^3\;dyne\;cm$

In CGS units Moment of force is dyne centimetre

In SI units the Moment of force is Newton meters

Hence,

Moment of Force or Torque (τ) in SI units is

⇒ 0.0064 Newton meter

$\red{\boxed{\boxed{\rm \tau = 0.0064\;Nm}}}$