A person pushes a box kept on a horizontal surface with force of $100 N$ . In unit vector notation force can be expressed as:

100 (^i +^j)

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100 (^i -^j)

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50 \sqrt{2} (^i -^j)

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50 \sqrt{2} (^i +^j)

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Solution

The correct option is C $50 \sqrt{2} (^i -^j)$

Component of force along $x - axis$
$F_{x} = F cos 45^{\circ}$
Component of force along $y - axis$
$F_{y} = F sin 45^{\circ}$
Net force on the box is
$\to F = F cos 45^{\circ}^i + F sin 45^{\circ} (-^j)$
$\Rightarrow \to F = 50 \sqrt{2}^i - 50 \sqrt{2}^j N$
$\Rightarrow \to F = 50 \sqrt{2} (^i -^j)$
Final Answer: (C)

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