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​

Answer 1

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

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Work Done = - 4π J

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The body moves from A to B .

Radius of semicircle = 4 cm

Radius of quadrant = 4 cm

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

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

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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 .

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• 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 .