Question

A block of mass $4\text{kg}$ is kept on a rough horizontal surface with coefficient of friction ${\mu }_s=0.4$ and ${\mu }_k=0.3$ and a time varying horizontal force $F=4t$ is applied on it. Then the acceleration - time graph of the particle is $(g=10{\text{m/s}}^2)$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

The FBD of the block is


From the FBD, we have
$N=4g=40\text{N}$
$(f_s{)}_{\text{max}}={\mu }_{s}N=0.4\times 40=16\text{N}$
and, $f_k={\mu }_{k}N=0.3\times 40=12\text{N}$

Now, the time for which block will remain static i.e $a=0$ is given by
$F<(f_s{)}_{\text{max}}$
$\Rightarrow 4t<16\Rightarrow t<4s$

and the time for which block will be in motion
$\Rightarrow F>(f_s{)}_{\text{max}}\Rightarrow t>4$

Acceleration of block after $t=4s$ is
$a=\frac{F-f_k}{m}=\frac{4t-12}{4}=t-3$
Hence, the variation $a$ is linear with $t$, and the minimum value will be at $t=4s$ which is
$a=t-3=4-3=1m/s^2$
Graph (b) is correct.