A body of mass $2 \mathrm{~kg}$ is on an inclined plane of inclination $30^{\circ}$ and coefficient of…

A body of mass $2 \mathrm{~kg}$ is on an inclined plane of inclination $30^{\circ}$ and coefficient of friction is $\left(\frac{1}{\sqrt{3}}\right)$. The minimum force required to move the body up the inclined plane is $\left(\right.$ Acceleration due to gravity $\left.=10 \mathrm{~ms}^{-2}\right)$
  1. $5.77 \mathrm{~N}$
  2. $10 \mathrm{~N}$
  3. $20 \mathrm{~N}$
  4. $15 \mathrm{~N}$

Solution

Mass of body, $m=2 \mathrm{~kg}$
For body moving up $ \begin{aligned} & F=m g \sin \theta+f_r \\ & =m g \sin \theta+\mu_k N=m g \sin \theta+\mu_k m g \cos \theta \\ & =2 \times 10 \times \frac{1}{2}+\frac{1}{\sqrt{3}} \times 2 \times 10 \times \frac{\sqrt{3}}{2}=20 N \end{aligned} $

Asked in: AP EAMCET 2023 (19 May Shift 1)

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