The relationship between the force F and position x of a body is shown in figure. The work done in displacing the body from x = 1 m to x =5 m will be

Question

The relationship between the force F and position x of a body is shown in figure. The work done in displacing the body from x = 1 m to x =5 m will be (A) 30 J (B) 15 J (C) 25 J (D) 20 J

Tardigrade Admin · Accepted Answer

Work done = area enclosed by F-x graph. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/20971c9cc72c24c0f208b3d2ae339d90-.png" /> = Area of O A M+ Area of A B N M+ Area of C D E N - Area of E F G H+ Area of H I J =(1/2) × 1 × 10+1 × 10+1 × 5-1 × 5+(1/2) × 1 × 10 =5 + 10 + 5 - 5 + 5 =20 J

Q. The relationship between the force $F$ and position $x$ of a body is shown in figure. The work done in displacing the body from $x = 1 m$ to $x = 5 m$ will be

$30 J$

$15 J$

$25 J$

$20 J$

Work done $=$ area enclosed by $F - x$ graph.

$=$ Area of $O A M +$ Area of $A BNM +$ Area of $C D EN$ $-$ Area of $EFG H +$ Area of $H I J$ $= \frac{1}{2} \times 1 \times 10 + 1 \times 10 + 1 \times 5 - 1 \times 5 + \frac{1}{2} \times 1 \times 10$
$= 5 + 10 + 5 - 5 + 5 = 20 J$

Q. The relationship between the force F and position x of a body is shown in figure. The work done in displacing the body from x=1m to x=5m will be

30J

15J

25J

20J