Statement I: If three force ${\vec{F}}_{1}, {\vec{F}}_{2} and {\vec{F}}_{3}$ are represented by three sides of triangle and ${\vec{F}}_{1} + {\vec{F}}_{2} = - {\vec{F}}_{3},$ then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement II: A triangle made up of three forces ${\vec{F}}_{1}, {\vec{F}}_{2} and {\vec{F}}_{3}$ as its sides taken in the same order, satisfy the condition for translator equilibrium.
In the light of the above statements, choose the most appropriate answer from the options given below:

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Both statement I and statement II are true

Statement I is true but statement II is false

Both statement I and statement II are false

Statement I is false but statement II is true

answer is D.

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Detailed Solution

If three force ${\vec{F}}_{1}, {\vec{F}}_{2} and {\vec{F}}_{3}$ are represented by three sides of triangle and ${\vec{F}}_{1} + {\vec{F}}_{2} = - {\vec{F}}_{3},$ then these three forces are not necessarily concurrent forces and satisfy the condition for translatory equilibrium only. They may not satisfy condition of rotational equilibrium.

A triangle made up of three forces ${\vec{F}}_{1}, {\vec{F}}_{2} and {\vec{F}}_{3}$ as its sides taken in the same order, will mean ${\vec{F}}_{1} + {\vec{F}}_{2} = - {\vec{F}}_{3},$ and it will satisfy the condition for translator equilibrium.