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Question

Physics Question on work, energy and power

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

A

8 J

B

11 J

C

5 J

D

2 J

Answer

5 J

Explanation

Solution

W=F⃗.dS⃗W = \vec{F} . \vec{dS}
=(4i^+3j^).[(4j^+3k^)−(−2i^+5j^)]= ( 4 \hat{i} + 3 \hat{j} ) . [(4 \hat{j} + 3 \hat{k}) - ( - 2 \hat{i} + 5 \hat{j})]
=(4i^+3j^).(2i^−j^+3k^)= ( 4 \hat{i} + 3 \hat{j}) . ( 2 \hat{i} - \hat{j} + 3 \hat{k})
=8−3=5J= 8 - 3 = 5 J