Question

The value of frictional force and acceleration of block of mass $10kg$ in the figure are
(Take $g=10{\text{m/s}}^2$)

• A. $10N,1m/s^2$
• B. $20N,2m/s^2$
• C. $20N,0m/s^2$
• D. $10N,0m/s^2$

Answer 1

The correct option is C $20N,0m/s^2$

Writing force equation using the FBD of the blocks,
For $4kg$ block, $T=4g$
For $10kg$ block in vertical direction,
$N+T\sin {60}^{\circ }=10g$
$\Rightarrow N=10g-T\sin {60}^{\circ }$
$N=10g-2g\sqrt{3}$

$f_{max}={\mu }_{s}N$
$=0.4[10g-2\sqrt{3}g]$
$=40-8\sqrt{3}N$

Horizontal force $T\cos {60}^{\circ }=20N<f_{max}$
Hence frictional force = $20N$ and system continues to be at rest.