Five forces F1→, F2→, F3→, F4→ and F5→ are acting on a particle of mass 2.0 kg so that it is moving with 4 m/s2 in east direction. If F1→ force is removed, then the acceleration becomes 7 m/s2 in north, then the acceleration of the block if only F1→ is acting will be:

F 1 → + F 2 → + F 3 → + F 4 → + F 5 → = 2(4 i ^ ) -------(i) and F 2 → + F 3 → + F 4 → + F 5 → = 2(7 j ^ ) ------(ii) From (i) and (ii), F 1 → = 8 i ^ - 14 j ^ a 1 → = F 1 → m = 4 i ^ -7 j ^ ⇒ a 1 = 16 + 49 = 65 m / s 2

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Five forces $\vec{F_{1}}$ , $\vec{F_{2}}$ , $\vec{F_{3}}$ , $\vec{F_{4}}$ and $\vec{F_{5}}$ are acting on a particle of mass 2.0 kg so that it is moving with 4 $m / s^{2}$ in east direction. If $\vec{F_{1}}$ force is removed, then the acceleration becomes 7 $m / s^{2}$ in north, then the acceleration of the block if only $\vec{F_{1}}$ is acting will be:

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16 $m / s^{2}$

$\sqrt{65}$ $m / s^{2}$

$\sqrt{33}$ $m / s^{2}$

$\sqrt{260}$ $m / s^{2}$

answer is .

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Detailed Solution

$\vec{F_{1}}$ + $\vec{F_{2}}$ + $\vec{F_{3}}$ + $\vec{F_{4}}$ + $\vec{F_{5}}$ = 2(4 $\hat{i}$ ) -------(i)

and $\vec{F_{2}}$ + $\vec{F_{3}}$ + $\vec{F_{4}}$ + $\vec{F_{5}}$ = 2(7 $\hat{j}$ ) ------(ii)

From (i) and (ii), $\vec{F_{1}}$ = 8 $\hat{i}$ - 14 $\hat{j}$

$\vec{a_{1}}$ = $\frac{\vec{F_{1}}}{m}$ = 4 $\hat{i}$ -7 $\hat{j}$

$\Rightarrow$ $a_{1}$ = $\sqrt{16 + 49}$ = $\sqrt{65}$ $m / s^{2}$

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