question_answer

The relationship between force and position is shown in the figure (in One dimensional case). Work done by the force is displacing a body from \[x\] = 1 cm to \[x\] = 5 cm is

A)  700 ergs

B)  70 ergs

C)  60 ergs

D)  20 ergs  

Correct Answer: D

Solution :

   Referring figure, work done by the force\[={{W}_{1}}+{{W}_{2}}+{{W}_{3}}+{{W}_{4}}\] where,\[{{W}_{1}}=\]area\[ABCM=1\times 10=10ergs\]           \[{{W}_{2}}=\]area\[MDEF=1\times 20=20ergs\]           \[{{W}_{3}}=\]area\[FGHI=1\times (-\text{ }20)=-20ergs\]           \[{{W}_{4}}=\]area\[IJKL=1\times 10=10ergs\] \[\therefore \]Net work done\[=10+20-20+10\] \[=\mathbf{20}\,\,\mathbf{ergs}\]