Answer
385.8k+ views
Hint: The amount of torque required to open the nut remains constant but the amount of force to be applied by the mechanic varies in the two cases. Therefore, the perpendicular distance of force from the position vector must also vary. We shall equate the torque in both cases since it is the constant quantity and find the new length of the handle.
Complete answer:
Let us suppose the body is fixed at a particular point. If we apply force on the body at some distance from this fixed point, then the body will rotate about the fixed point. This force that is applied a distance away from the pivot point (or we could say the axis of rotation or centre of mass) is called torque.
Torque is a vector quantity. It consists of both magnitude and direction.
Thus, torque is defined as force times distance. It is the force that is perpendicular to the object, that is, the component of force is perpendicular to the position vector.
$\tau =F\times r$
The unit of torque is Newton. Meters, $\left( Nm \right)$.
Torque, $\tau =$ constant
$\Rightarrow {{F}_{1}}\times {{r}_{1}}={{F}_{2}}\times {{r}_{2}}$
Where,
${{F}_{1}}=$ force applied in the first case
${{F}_{2}}=$ force applied in the second case
${{r}_{1}}=$ length of lever handle in first case
${{r}_{2}}=$ length of lever handle in second case
Now, we have ${{F}_{1}}=F,{{F}_{2}}=\dfrac{2F}{3},{{r}_{1}}=h$,
$\begin{align}
& \Rightarrow F\times h=\dfrac{2F}{3}\times {{r}_{2}} \\
& \Rightarrow {{r}_{2}}=\dfrac{3h}{2} \\
\end{align}$
Therefore, the length of the lever required is $\dfrac{3h}{2}$.
Hence, the correct option is (B) $\dfrac{3h}{2}$.
Note:
The centre of mass of a body or a system of bodies is expressed as the point where all the mass of the body seems to be concentrated and is at equilibrium. Thus, if we apply force on the centre of mass of a body, the whole body accelerates in the direction of the force applied.
Complete answer:
Let us suppose the body is fixed at a particular point. If we apply force on the body at some distance from this fixed point, then the body will rotate about the fixed point. This force that is applied a distance away from the pivot point (or we could say the axis of rotation or centre of mass) is called torque.
Torque is a vector quantity. It consists of both magnitude and direction.
Thus, torque is defined as force times distance. It is the force that is perpendicular to the object, that is, the component of force is perpendicular to the position vector.
$\tau =F\times r$
The unit of torque is Newton. Meters, $\left( Nm \right)$.
Torque, $\tau =$ constant
$\Rightarrow {{F}_{1}}\times {{r}_{1}}={{F}_{2}}\times {{r}_{2}}$
Where,
${{F}_{1}}=$ force applied in the first case
${{F}_{2}}=$ force applied in the second case
${{r}_{1}}=$ length of lever handle in first case
${{r}_{2}}=$ length of lever handle in second case
Now, we have ${{F}_{1}}=F,{{F}_{2}}=\dfrac{2F}{3},{{r}_{1}}=h$,
$\begin{align}
& \Rightarrow F\times h=\dfrac{2F}{3}\times {{r}_{2}} \\
& \Rightarrow {{r}_{2}}=\dfrac{3h}{2} \\
\end{align}$
Therefore, the length of the lever required is $\dfrac{3h}{2}$.
Hence, the correct option is (B) $\dfrac{3h}{2}$.
Note:
The centre of mass of a body or a system of bodies is expressed as the point where all the mass of the body seems to be concentrated and is at equilibrium. Thus, if we apply force on the centre of mass of a body, the whole body accelerates in the direction of the force applied.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)