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Home  >>  JEEMAIN and AIPMT  >>  Physics  >>  Class11  >>  Laws of Motion
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An object experiences an acceleration of magnitude $3.75 m/s^2$. Calculat the mass of the object given there are three forces acting on an object as follows:

$\overrightarrow{F1} = (-2\overrightarrow{i}+ 2\overrightarrow{j})\; N$
$\overrightarrow{F2} = (5\overrightarrow{i}-3\overrightarrow{j})\; N$
$\overrightarrow{F3} = (-45\overrightarrow{i})\; N$
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  • According to Newton's second law: When viewed from an inertial reference frame, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Answer: 11.2 Kg
According to Newton's second law, $\large\Sigma $$F = \overrightarrow{F1} + \overrightarrow{F2} + \overrightarrow{F3} = m\overrightarrow{a}$
$\Rightarrow \large\Sigma$$ F = (-2\overrightarrow{i}+ 2\overrightarrow{j})\; +(5\overrightarrow{i}-3\overrightarrow{j})\; + (-45\overrightarrow{i})\; $
$\Rightarrow \large\Sigma$$F =(-42\overrightarrow{i} -\overrightarrow{j})N$
$\Rightarrow |\Sigma F| = \sqrt{F_x^2 + F_y^2} = \sqrt{42^2+1^2} = 42.012\;N$
$\Rightarrow$ Mass $ = \large\frac{|\Sigma F|}{a} $$ = \large\frac{42.012\;N}{3.75 \;m/s^2}$$ = 11.2032\;Kg$
answered Aug 19, 2014 by balaji.thirumalai
edited Aug 19, 2014 by balaji.thirumalai

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