Question 176 of 210

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: $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$

A$4 \mathrm{~N}$B$14 \mathrm{~N}$C$6 \mathrm{~N}$D$20 \mathrm{~N}$

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Answer: (D) $20 \mathrm{~N}$

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 $F$
$$\begin{aligned} &F-M g \sin \theta-f=M a \\ &\Rightarrow F-10-4=6 \\ &F=20 \mathrm{~N} \end{aligned}$$