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Question: ABCDE is pentagon. Forces acting on a particle are represented in magnitude and direction by \(\ove...

ABCDE is pentagon. Forces acting on a particle are represented in magnitude and direction by

AB→,BC→,CD→,2DE→,AD→,\overset{\rightarrow}{AB},\overset{\rightarrow}{BC},\overset{\rightarrow}{CD},2\overset{\rightarrow}{DE},\overset{\rightarrow}{AD}, andAE→\overset{\rightarrow}{AE}. Their resultant is given by

A

AE→\overset{\rightarrow}{AE}

B

2AB→2\overset{\rightarrow}{AB}

C

3AE→3\overset{\rightarrow}{AE}

D

4AE→4\overset{\rightarrow}{AE}

Answer

3AE→3\overset{\rightarrow}{AE}

Explanation

Solution

We have, AB→+BC→+CD→+2DE→+AD→+AE→\overset{\rightarrow}{AB} + \overset{\rightarrow}{BC} + \overset{\rightarrow}{CD} + 2\overset{\rightarrow}{DE} + \overset{\rightarrow}{AD} + \overset{\rightarrow}{AE}

=(AB→+BC→)+(CD→+DE→)+(AD→+DE→)+AE→\left( \overset{\rightarrow}{AB} + \overset{\rightarrow}{BC} \right) + \left( \overset{\rightarrow}{CD} + \overset{\rightarrow}{DE} \right) + \left( \overset{\rightarrow}{AD} + \overset{\rightarrow}{DE} \right) + \overset{\rightarrow}{AE}

=(AC→+CE→)+AE→+AE→\left( \overset{\rightarrow}{AC} + \overset{\rightarrow}{CE} \right) + \overset{\rightarrow}{AE} + \overset{\rightarrow}{AE} =AE→+AE→+AE→=3AE→\overset{\rightarrow}{AE} + \overset{\rightarrow}{AE} + \overset{\rightarrow}{AE} = 3\overset{\rightarrow}{AE}.