First slide

Newton's laws of motion

Question

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/s² in east direction. If ${\vec{F}}_{1}$ force is removed, then the acceleration becomes 7 m/s² in north, then the acceleration of the block if only ${\vec{F}}_{1}$ is acting will be

Moderate

A

$16 m / s^{2}$
B

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

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

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

Solution

$\begin{array}{l} {\vec{F}}_{1} + {\vec{F}}_{2} + {\vec{F}}_{3} + {\vec{F}}_{4} + {\vec{F}}_{5} = 2 (4 \hat{i}) . . . . . . . (i) \\ and {\vec{F}}_{2} + {\vec{F}}_{3} + {\vec{F}}_{4} + {\vec{F}}_{5} = 2 (7 \hat{j}) . . . . . . . . (i i) \end{array}$
$From (i) and (ii), {\vec{F}}_{1} = 8 \hat{i} - 14 \hat{j}$
$\begin{array}{l} {\vec{a}}_{1} = \frac{{\vec{F}}_{1}}{m} = 4 \hat{i} - 7 \hat{j} \\ \Rightarrow a_{1} = \sqrt{16 + 49} = \sqrt{65} m / s^{2} \end{array}$

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