Question

A wheel of diameter 2 m can be rotated about an axis passing through its centre by a moment of force equal to 2.0 N m. What minimum force must be applied on its rim ?​

Answer 1

To Find :-

The Minimum Force applied on the rim.

Given :-

• Diameter of the wheel :- 2 m

• Moment of force or torque = 2 N m

We know :-

Moment of Force / Torque :-

$\underline{\boxed{\bf{Torque (\tau) = Force \times Perpendicular\:Distance}}}$

Radius of a Circle :-

$\underline{\boxed{\bf{Radius = \dfrac{Diameter}{2}}}}$

Concept :-

We know that a object rotate at a pivoted point , and in the this case the wheel rotate around the radius the Circle , but the diameter of the Circle is given , so by using the Formula for Radius of a circle , we can find the required value.

Given , the diameter is 2 m , so substituting the given value in the formula , we get :-

$:\implies\bf{Radius = \dfrac{Diameter}{2}} \\ \\ \\ :\implies\bf{Radius = \dfrac{2}{2}} \\ \\ \\ :\implies \bf{Radius = 1} \\ \\ \\ \therefore \purple{\bf{Radius = 1 m}}$

Now by this information, we can find the Force applied on the rim.

Solution :-

Given :-

• Perpendicular Distance = 1 m

• Moment of Force or Torque = 2 N m

Let the Force applied be F N.

Now ,

By using the formula for Torque and substituting the values in it , we get :-

$:\implies \bf{Torque = Force \times Perpendicular\:Distance} \\ \\ \\ :\implies \bf{2 = F \times 1} \\ \\ \\ :\implies \bf{\dfrac{2}{1} = F} \\ \\ \\ :\implies \bf{2 = F} \\ \\ \\ \therefore \purple{\bf{F = 2 N}}$

Hence, the force applied is 2 N.

Answer 2

$\mathfrak{\red{\underline{Given:-}}}$

• A wheel of diameter 2 m can be rotated about an axis passing through its centre by a moment of force equal to 2.0 N m.

$\mathfrak{\blue{\underline{To \: find:-}}}$

• What minimum force must be applied on its rim ?

$\underline{\orange{Formula :-}}$

Moment of Force / Torque :-

$\underline{\pink{\boxed{\bf{Torque (\tau) = Force \times Perpendicular\:Distance}}}}$

Radius of a Circle :-

$\underline{\pink{\boxed{\bf{Radius = \dfrac{Diameter}{2}}}} }$

$\green{\underline{SOLUTION:-}}$

Given , the diameter is 2 m , so substituting the given value in the formula , we get :-

$\begin{gathered}\implies\bf{Radius = \dfrac{Diameter}{2}} \\ \\ \implies\bf{Radius = \dfrac{2}{2}} \\ \\ \implies \bf{Radius = 1} \\ \\ {\bf{Radius = 1 m}}\end{gathered}$

Given,

• Perpendicular Distance = 1 m

• Moment of Force or Torque = 2 N m

• Let the Force applied be F N.

Now ,

$\implies Torque = Force \times Perpendicular\:Distance$

$\implies \bf{2 = F \times 1}$

$\implies \bf{\dfrac{2}{1} = F}$

$\implies \bf{2 = F} \\ \\ \\ \therefore \blue{\bf{F = 2 N}}$

Hence, $\underline{\orange{the \:force\: applied\: = 2 N.}}$

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