Question

A block of mass 5 kg is lying on a rough horizontal surface. The coefficients of static and kinetic friction between the block and the surface respectively are 0.7 and 0.5. A horizontal force just sufficient to move the block is applied to it. If the force continues to act even after the block has started moving, what will be the acceleration of the block? Take $g=10m{s}^{-2}$.

• A. $1m{s}^{-2}$
• B. $2m{s}^{-2}$
• C. $3m{s}^{-2}$
• D. $4m{s}^{-2}$

Answer 1

The correct option is B

$2m{s}^{-2}$

Given $m=5kg$,
${\mu }_s=0.7$ and
${\mu }_k=0.5$
Force required to just move the block = Limiting friction, i.e., $F={\mu }_{s}mg=0.7\times 5\times 10=35N$
Now, once the block starts moving, kinetic friction will act on it. The accelerating force will be given by the difference of applied force and kinetic friction.
$F_a=F-{\mu }_{k}mg=35-0.5\times 5\times 10=35-25=10N$
Acceleration, $a=\frac{F_a}{m}=\frac{10}{5}=2m{s}^{-2}$
Hence, the correct choice is (b).