Question

A block is placed over a large plank (plank is kept on horizontal surface). The coefficient of friction between the block and the plank is $\mu =0.2$. Initially both are at rest, suddenly the plank starts moving horizontally with acceleration $a_0=4m/s^2$ with the help of some external force. The displacement of the block in 1s is $(g=10m/s^2)$

• A. $1m$ relative to ground
• B. $1m$ relative to plank
• C. zero relative to plank
• D. $2m$ relative to ground

Answer 1

The correct option is B $1m$ relative to plank

Let the mass of block be $m$ and the mass of plank be $M$
Considering the motion of block w.r.t plank, we have from the figure,

$4m-\mu mg=ma$

$\Rightarrow 4-\mu g=a$

$\Rightarrow a=4-\left(0.2\right)\left(10\right)$

$\Rightarrow a=4-2=2m/se{c}^2$

Using,
$s=ut+\frac{1}{2}a{t}^2$, we have,

$u=0m/sec$

$a=2m/se{c}^2$

$t=1sec$
$s=0+\frac{1}{2}\left(2\right)(1{)}^2$

$s=1m$, relative to plank

Hence, the correct answer is OPTION B.