Two forces F1→ and F2→ are acting on a body. The body is found to move along positive x-axis with acceleration 3 m/s2.. When F2→ is reversed, the body is found to move along positive y-axis with acceleration 4 m/s2. What will be the acceleration of the body if only F1→ acts on it?

F1→ + F2→ = 3m i^F1→ - F2→ = 4m j^ Adding, 2F1→ = m3i^ + 4j^⇒F1→ m = 123i^ + 4j^ m/s2∴ a= F→1 m = 52 m/s2 =2.5 m/s2

Two forces F1→ and F2→ are acting on a body. The body is found to move along positive x-axis with acceleration 3 m/s2.. When F2→ is reversed, the body is found to move along positive y-axis with acceleration 4 m/s2. What will be the acceleration of the body if only F1→ acts on it?

F1→ + F2→ = 3m i^F1→ - F2→ = 4m j^ Adding, 2F1→ = m3i^ + 4j^⇒F1→ m = 123i^ + 4j^ m/s2∴ a= F→1 m = 52 m/s2 =2.5 m/s2

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Two forces $\vec{F_{1}} and \vec{F_{2}}$ are acting on a body. The body is found to move along positive x-axis with acceleration $3 m / s^{2} .$ . When $\vec{F_{2}}$ is reversed, the body is found to move along positive y-axis with acceleration $4 m / s^{2}$ . What will be the acceleration of the body if only $\vec{F_{1}}$ acts on it?

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$2.5 m / s^{2}$

$5 m / s^{2}$

$6.5 m / s^{2}$

$1.5 m / s^{2}$

answer is A.

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Detailed Solution

$\begin{array}{l} \vec{F_{1}} + \vec{F_{2}} = 3 m \hat{i} \\ \vec{F_{1}} - \vec{F_{2}} = 4 m \hat{j} \end{array}$
$Adding, 2 \vec{F_{1}} = m (3 \hat{i} + 4 \hat{j})$

$\Rightarrow \frac{\vec{F_{1}}}{m} = \frac{1}{2} (3 \hat{i} + 4 \hat{j}) m / s^{2}$

$∴ a = \frac{|{\vec{F}}_{1}|}{m} = \frac{5}{2} m / s^{2} = 2 .5 m / s^{2}$

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Two forces F1→ and F2→ are acting on a body. The body is found to move along positive x-axis with acceleration 3 m/s2.. When F2→ is reversed, the body is found to move along positive y-axis with acceleration 4 m/s2. What will be the acceleration of the body if only F1→ acts on it?

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