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We can arrange four different situations where a particle is acted upon by three forces. In each case their magnitudes are proportional to $(i) 3, 5, 8; (i i) 5, 7, 10; (i i i) 3, 5, 10$ and $(i v) 5, 7, 14;$ in which cases can the particle be at rest ?

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Case $(i)$

Case $(i i)$

Case $(i i i)$

Case $(i v)$

answer is A, B.

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Detailed Solution

(iii) is not possible because the magnitude of resultant of 3 and 5

$(i v)$ is not possible because the magnitude of resultant of $5$ and $7$ will lie between $2$ and $12$ . So it can’t balance $14 N$ force. Net force will not be zero in this case.

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