Work Energy And Power Question 232
Question: The components of a force acting on a particle are varying according to the graphs shown. When the particles move from (0,5,6) to (2,10,0) then the work done by this force is
Options:
A) 192J
B) $ \frac{400}{3}J $
C) $ \frac{287}{2}J $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] From given graph: $ \vec{F}=( \frac{3}{4}x+10 )\hat{i}+( 20-\frac{4}{3}y )\hat{j}+( \frac{4}{3}z-16 )\hat{k} $
$ W=\int{\vec{F}.\overrightarrow{ds}} $
$ =\int\limits _{( 0,5,6 )}^{( 2,10,0 )}{( \frac{3}{4}x+10 )\hat{i}+( 20-\frac{4}{3}y )\hat{j}+( \frac{4}{3}z-16 )\hat{k}} $
$ [dx\hat{i}+dy\hat{j}+dz\hat{k}]=\frac{287}{2}J $ Work done can also be found by finding area under these curves.
