Question

Pls solve this
The figure represents F/x graph Find work done to move a body from A to B under action of variable force
Pls ans this
Yaar tumlog spam itna karte ho isse accha ans hi kardo bhai, pata nahi spam karne mei kya maza aata hai kabse puch rahe hai ek dhang ka ans nahi mila hai mereko​

Answer 1

Answer:

• -4π Joules is the required work done .

Explanation:

According to the Question

It is given that figure represents F/x graph Find work done to move a body from A to B under action of variable force.

we have to calculate the work done to move a body from A to B . And also variable force is acting on it .

As we know that ,

• Area under F/x graph = Work done

Firstly we calculate the area of bigger semicircle .

Radius of bigger semicircle = 4

➻ Area of semicircle,A1 = π4²/2

➻ Area of Semicircle ,A1 = 16π/2

➻ Area of Semicircle ,A1 = 8π

Now, calculating the area from O to B .

As we can say that 1/4th part of circle .

➻ Area ,A2 = π4²/4

➻ Area ,A2 = 16π/4

➻ Area ,A2 = 4π

Now, calculating the total work done by the body .

As we know that work done is a vector quantity. It means that its has direction as well as magnitude .

From Figure we observe that the body goes from Right to left side . A to B .

So,

• Total Work Done = A1 + A2

substitute the value from above we get

➻ Total Work Done = -8π + 4 π

➻ Total Work Done = -4π J

• Hence, the total work done to move body from A to B is -4π J .

Answer 2

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

The figure represents Force - Displacement graph . Find work done to move a body from A to B under action of variable force .

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

• Work Done = - 4π J

$\huge\purple{ \underline{ \boxed{\mathbb{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

• The body moves from A to B .

• Radius of semicircle = 4 cm

• Radius of quadrant = 4 cm

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

Work done to move body from A to B under action of variable force .

$\green{ \large \underline{ \mathbb{\underline{FORMULAS \: USED: }}}}$

$\purple{ \boxed{ \begin{array}{l} \bigstar \: \textsf{Work Done = Fs} \: \\ \\ \hline \\ \bigstar \: \textsf{Area of semicircle = \displaystyle \sf \frac{\pi {r}^{2}}{2} } \\ \\ \hline \\\bigstar \: \textsf{Area of quadrant = \displaystyle \sf \frac{\pi {r}^{2}}{4} } \end{array}}}$

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

We know that area under force - displacement graph gives work done . Therefore ,

$\red{\textsf{ \underline{\underline{Area of semicircle OA : }}}}$

$\textsf{Area of semicircle = \displaystyle \sf \frac{\pi {r}^{2}}{2} }$

$\displaystyle \sf \longrightarrow \frac{\pi {(4)}^{2} }{2} \: \: \: \\ \\ \displaystyle \sf \longrightarrow \frac{\pi \times 16}{2} \: \\ \\ \displaystyle \sf \longrightarrow \frac{\pi \times \cancel{16}}{ \cancel{2 }} \: \\ \\ \displaystyle \sf \longrightarrow\pi \times 8 \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow8\pi \: \: \: \: \: \: \: \:$

$\red{\textsf{ \underline{\underline{Area of quadrant OB : }}}}$

$\textsf{Area of quadrant = \displaystyle \sf \frac{\pi {r}^{2}}{4} }$

$\displaystyle \sf \longrightarrow \frac{\pi {(4)}^{2} }{4} \: \: \: \\ \\ \displaystyle \sf \longrightarrow \frac{\pi \times 16}{4} \: \\ \\ \displaystyle \sf \longrightarrow \frac{\pi \times \cancel{16}}{ \cancel{4 }} \: \\ \\ \displaystyle \sf \longrightarrow\pi \times 4 \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow4\pi \: \: \: \: \: \: \: \: \:$

From figure , We see that body is moving from right to left . Therefore , Work done from A to O becomes negative . The work done from O to B is also negative but the quadrant is also negative . Therefore , negative signs cancel each other .

• Work done = ( - 8π + 4π ) J

• Work done = - 4π J

Hence , Work done to move body from A to B under action of variable force is -4π Joule .

$\green{ \large \underline{ \mathbb{\underline{KNOW\:MORE: }}}}$

• Force

Force is the push or pull on an object with mass that causes it to change its velocity.

• Displacement

Displacement is the shortest distance between initial and final position of the object .

• Work Done

Work is said to be done by a force on an object only when the object moves in any direction except in the direction perpendicular to the force .

• Joule

One joule is defined as the work done by one newton force in moving an object through a distance of one metre along the direction of applied force .