A particle moves from a point ( - 2 i + 5 j ) to ( 4 i + 3 j ) wh… - Vidyadip

MCQ

A particle moves from a point $\left( { - 2\hat i + 5\hat j} \right)$ to $\left( {4\hat i + 3\hat j} \right)$ when a force of $\left( {4\hat j + 3\hat k} \right)$ is applied. How much work has been done by the force ?......$J$

✓
$5$
B
$2$
C
$8$
D
$11$

✓

Answer

Correct option: A.

$5$

a
$\begin{array}{l}
\,\,\,\,\,Here\,\overrightarrow r = \left( { - 2\hat i + 5\hat j} \right)m,\,{\overrightarrow r _2} = \left( {4\hat j + 3\hat k} \right)m\\
\overrightarrow F = \left( {4\hat i + 3\hat j} \right)\,N,\,W = ?\\
Work\,done\,by\,force\,F\,in\,moving\,from\\
{\overrightarrow r _1}\,to{\overrightarrow {\,r} _2},\\
W = \overrightarrow F .\left( {\overrightarrow {{r_2}} - \overrightarrow {{r_1}} } \right)\\
\Rightarrow W = \left( {4\hat i + 3\hat j} \right).\left( {4\hat j + 3\hat k + 2\hat i - 5\hat j} \right)\,\,\\
= \left( {4\hat i + 3\hat j} \right).\left( {2\hat i - \hat j + 3\hat k} \right) = 8 + \left( { - 3} \right) = 5\,J
\end{array}$

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