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  • Consider a block kept on an inclined plane (inclined at ) as shown in the figure. If the force

Consider a block kept on an inclined plane (inclined at 45^{\circ}) as shown in the figure. If the force
required to just push it up the incline is 2 times the force required to just prevent it from sliding down,
the coefficient of friction between the block and inclined plane (\mu) is equal to :

Option: 1

0.25


Option: 2

0.50


Option: 3

0.60


Option: 4

0.33


Answers (1)

 
\begin{aligned} & \mathrm{F}_1=\mathrm{mg} \sin \theta+\mu \mathrm{mg} \cos \theta \\ & \mathrm{F}_1=\mathrm{mg} \sin 45+\mu \mathrm{mg} \cos 45 \\ & \mathrm{~F}_2=\mathrm{mg} \sin 45-\mu \mathrm{mg} \cos 45 \end{aligned}
\begin{aligned} & \mathrm{F}_1=2 \mathrm{~F}_2 \\ & \mathrm{mg}\left(\frac{1}{\sqrt{2}}+\frac{\mu}{\sqrt{2}}\right)=2 \mathrm{mg}\left(\frac{1}{\sqrt{2}}-\frac{\mu}{\sqrt{2}}\right) \\ & 1+\mu=2-2 \mu \\ & 3 \mu=1 \\ & \mu=\frac{1}{3}=0.33 \end{aligned}

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Kshitij

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