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

(A) Statement-I is false but Statement-II is true

(B) Statement-I is true but Statement-II is false

(C) Both Statement-I and Statement-II are false

JEE Mains · Physics · STD 11 - Vectors

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

Pick an option to check your answer.

Verified Solution

Correct Answer

(D) Both Statement\(-I\) and Statement\(-II\) are true.

Detailed explanation

Here \(\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}+\overrightarrow{{F}}_{3}=0\)

\(\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}\)

Since \(\overrightarrow{{F}}_{\text {net }}=0\) (equilibrium)

Both statements correct

Same subject

From JEE Mains

List-I	List-II
A. \(\sin^2 \omega t\)	I. Periodic with time period \(T = \dfrac{\pi}{\omega}\) but not simple harmonic motion (SHM)
B. \(\sin^3(2\omega t)\)	II. Periodic with time period \(T = \dfrac{2\pi}{\omega}\) but Not SHM
C. \(\sin(\omega t) + \cos(\pi \omega t)\)	III. Periodic with time period \(T = \dfrac{\pi}{\omega}\) and SHM
D. \(\cos\omega t + \cos 2\omega t\)	IV. Non-periodic