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NEET · Physics · STD 11 - 5. work,energy,power and collision
A particle moves from a point \(\left( { - 2\hat i + 5\hat j} \right)\) to \(\left( {4\hat j + 3\hat k} \right)\) when a force of \(\left( {4\hat i + 3\hat j} \right)\) is applied. How much work has been done by the force ?......\(J\)
- A \(5\)
- B \(2\)
- C \(8\)
- D \(11\)
Answer & Solution
Correct Answer
(A) \(5\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{l}
\,\,\,\,\,Here\,\overrightarrow r = \left( { - 2\hat i + 5\hat j} \right)m,\,{\overrightarrow r _2} = \left( {4\hat j + 3\hat k} \right)m\\
\overrightarrow F = \left( {4\hat i + 3\hat j} \right)\,N,\,W = ?\\
Work\,done\,by\,force\,F\,in\,moving\,from\\
{\overrightarrow r _1}\,to{\overrightarrow {\,r} _2},\\
W = \overrightarrow F .\left( {\overrightarrow {{r_2}} - \overrightarrow {{r_1}} } \right)\\
\Rightarrow W = \left( {4\hat i + 3\hat j} \right).\left( {4\hat j + 3\hat k + 2\hat i - 5\hat j} \right)\,\,\\
= \left( {4\hat i + 3\hat j} \right).\left( {2\hat i - \hat j + 3\hat k} \right) = 8 + \left( { - 3} \right) = 5\,J
\end{array}\)
\,\,\,\,\,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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