A block of mass $m$ is moving on a rough horizontal surface. The coefficient of kinetic friction between…

A block of mass $m$ is moving on a rough horizontal surface. The coefficient of kinetic friction between block and surface is $\mu_{k}$, The net force exerted by the surface on the block is $\quad(\mathrm{g}=$ acceleration due to gravity $)$
  1. $\operatorname{mg}\left(1+\mu_{\mathrm{k}}\right)^{1 / 2}$
  2. $\left[\mathrm{mg}\left(1+\mu_{\mathrm{k}}\right)\right]^{1 / 2}$
  3. $\mathrm{mg}\left(1+\mu_{\mathrm{k}}^{2}\right)$
  4. $\mathrm{mg}\left(1+\mu_{\mathrm{k}}^{2}\right)^{1 / 2}$

Solution

Given that: If body of mass \(m\) moving with rough horizontal surface Kinetic fiction = u \(\begin{aligned} F_{\text {net }} &=\sqrt{f_{1}^{2}+f_{3}{ }^{2}} \\ &=\sqrt{\left(m g^{2}\right)^{2}+(l m g)^{2}} \end{aligned}\) \(F=m g \sqrt{1+\mu^{2}}=\) option \(A\) is correct

Asked in: MHT CET 2020 (15 Oct Shift 2)

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