Work Energy And Power Question 215
Question: A uniform force of $ ( 3\hat{i}+\hat{k} ) $ newton acts on a article of mass 2 kg. The particle is displaced from position $ ( 2\hat{i}+\hat{k} ) $ meter to position $ ( 4\hat{i}+3\hat{j}-\hat{k} ) $ meter. The work done by the force on the particle is
Options:
A) 6 J
B) 13 J
C) 15 J
D) 9 J
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Given : $ \vec{F}=3\hat{i}+\hat{j} $
$ {{\vec{r}}_1}=( 2\hat{i}+\hat{k} ),{{\vec{r}}_2}=( 4\hat{i}+3\hat{j}-\vec{k} ) $
$ {{\vec{r}}_1}={{\vec{r}}_2}-{{\vec{r}}_1}=( 4\hat{i}+3\hat{j}-\vec{k} )-( 2\hat{i}+\hat{k} ) $
$ or \vec{r} = 2\hat{i}+3\hat{j} - 2\hat{k} $ So work done by the given force $ w = \vec{f}.\vec{r} $
$ = (3\hat{i}+\hat{j}).(2\hat{i}+3\hat{j}-2\vec{k})=6+3=9J $
