Question

A plank of mass $2kg$ and length $1m$ is placed on horizontal floor. A small block of mass 1 kg is placed on top of the plank at its right extreme end. The coefficient of friction between plank and floor is $0.5$ and that between plank and block is $0.2$. If a horizontal force = $30N$starts acting on the plank to the right, the time after which the block will fall off the plank is
$(g=10m{s}^{-2})$

• A. 2/3
• B. 1.5s
• C. 0.75 s
• D. 4/3

Answer 1

The correct option is A 2/3

let $f_1$ be the maximum limiting friction provided by floor and plank $\mu mg=0.5\times 30=15N$

similarly limiting friction provided between plank and block $f_2=0.2\times 10=2N$

for plank: acceleration $A=\frac{F-f_1-f_2}{M}=\frac{30-15-2}{2}=6.5m/s^2$

for block: acceleration $a=\frac{f_2}{m}=2m/s^2$

relative acceleration $a_{rel}=4.5m/s^2$

so $l=\frac{1}{2}{a}_{rel}{t}^2$

which gives $t=2/3sec$