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A system of two blocks of masses $\mathrm{m= 2kg}$ and $\mathrm{M= 8kg}$ is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $\mathrm{0.5}$ . The maximum horizontal force $\mathrm{F}$ that can be applied to the block of mass $\mathrm{M}$ so that the block move together will be :

Option: 1
$\mathrm{9.8N}$

Option: 2
$\mathrm{39.2N}$

Option: 3
$\mathrm{49N}$

Option: 4
$\mathrm{78.4N}$

Answers (1)

$\mathrm{f_{l } =\mu \mathrm{~N}} \\$

$\mathrm{=0.5 \times 20=10 \mathrm{~N}}$

Let both blocks are moving without slipping then

$\mathrm{ F=(2+8) \times a \\ }\\$

$\mathrm{a=\frac{F}{10}}$

For the upper block,

$\mathrm{f=m a \leq f _ { l } }\\$

$\mathrm{2 \times \frac{F}{10} \leqslant 10 }\\$

$\mathrm{F \leqslant 50 \mathrm{~N}}$

Hence the correct answer is option 3.

Posted by

Sumit Saini

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