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A body of mass $2 \mathrm{~kg}$ slides down with an acceleration of $3 \mathrm{~m} / \mathrm{s}^2$ on a rough inclined plane having a slope of $30^{\circ}$. The external force required to take the same body up the plane with the same acceleration will be: $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$
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Verified Answer
The correct answer is:
$20 \mathrm{~N}$
$20 \mathrm{~N}$
Equation of motion when the mass slides down
$$
\begin{aligned}
&M g \sin \theta-f=M a \\
&\Rightarrow 10-f=6 \\
&\quad\left(M=2 \mathrm{~kg}, a=3 \mathrm{~m} / \mathrm{s}^2, \theta=30^{\circ} \text { given }\right) \\
&\therefore f=4 \mathrm{~N}
\end{aligned}
$$
{ Equation of motion when the block is }
pushed up
Let the external force required to take the block up the plane with same acceleration be $F$
$$
\begin{aligned}
&F-M g \sin \theta-f=M a \\
&\Rightarrow F-10-4=6 \\
&F=20 \mathrm{~N}
\end{aligned}
$$
$$
\begin{aligned}
&M g \sin \theta-f=M a \\
&\Rightarrow 10-f=6 \\
&\quad\left(M=2 \mathrm{~kg}, a=3 \mathrm{~m} / \mathrm{s}^2, \theta=30^{\circ} \text { given }\right) \\
&\therefore f=4 \mathrm{~N}
\end{aligned}
$$
{ Equation of motion when the block is }
pushed up
Let the external force required to take the block up the plane with same acceleration be $F$
$$
\begin{aligned}
&F-M g \sin \theta-f=M a \\
&\Rightarrow F-10-4=6 \\
&F=20 \mathrm{~N}
\end{aligned}
$$
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