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  • Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are<div class='qna-option

Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are

Option: 1

12 N, 6 N


Option: 2

13 N, 5 N


Option: 3

10 N, 8 N


Option: 4

16 N, 2 N


Answers (1)

best_answer

Resultant  R is perpendicular to smaller force  Q and (P+Q) = 18 N

\therefore \: \: P^{2}= Q^{2}+R^{2}\: \: by\: right \: angled\: triangle

or    \left ( P^{2}-Q^{2} \right )= R^{2}

or    \left ( P+Q \right )\: \left ( P-Q \right )= R^{2}

or    \left ( 18 \right )\left ( P-Q \right )= \left ( 12\right )^{2}            \because \: \: \left [ P+Q= 18 \right ]

or    \left ( P-Q \right )= 8

Hence P= 13\: N\: \: and\: \: Q= 5\: N

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Riya

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