The relationship between the force F and position x of a body is as 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 as 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 = area of ABNM + area of CDEN - area of EFGH + area of HIJ = 1 × 10 + 1 × 5 + (1/2) × 1 × 10 = 10 + 5 - 5 + 5 = 15 J

Q. The relationship between the force $F$ and position $x$ of a body is as 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 $A BNM$ + area of $C D EN$ - area of $EFG H$ + area of $H I J$
$= 1 \times 10 + 1 \times 5 + \frac{1}{2} \times 1 \times 10$
$= 10 + 5 - 5 + 5 = 15 J$

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