Question

A block B of mass $4$kg is placed on a rough horizontal plane. A time dependent horizontal force $f=k{t}^2$ acts on the block, $k=2N/s^2$. The frictional force between the block and the plane at $t=2$ sec is $\mu =0.2$

• A. $4$N
• B. $8$N
• C. $12$N
• D. zero

Answer 1

The correct option is B $8$N

$F={4t}^2$

$F={2t}^2-4=2$

$F_{max}=\mu mg$

$=\left(0.8\right)\left(4\right)\left(10\right)$

$=32N$.

Applied Force $F={2t}^2$

at $t=2s$ $F=2{\left(2\right)}^2=8N$

Hence body cannot move and force of friction between block and phase $=$ applied force $=8N$.