Question

A block of mass $4\text{kg}$ is placed on a rough horizontal plane. A time depedent force $F=k{t}^2$ acts on the block, where $k=2{\text{N/s}}^2$. Coefficient of static friction $\mu =0.8$. Force of friction between the block and the plane at $t=2\text{s}$ is

• A. $8\text{N}$
• B. $4\text{N}$
• C. $2\text{N}$
• D. $32\text{N}$

Answer 1

The correct option is A $8\text{N}$

$f_{\text{max}}=\mu mg=0.8\times 4\times 10=32\text{N}$
At $t=2\text{s}$, $F=k{t}^2=\left(2\right)(2{)}^2=8\text{N}$

Since applied force $f_{t=2}<f_{\text{max}}$, block will be at rest and force of friction will be applied force at $t=2\text{s}$ which is $8\text{N}$