Question

A block is placed over a large plank (plank is kept on the 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 the acceleration $a_0=4m/s^2$ with the help of some external force. The displacement of the block in 1s is (g = 10 $m/s^2$)

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

Answer 1

The correct option is A 1 m relative to ground

Friction on $m$ mass block is $f$.

$f=\mu mg=0.2mg$

$F=m{a}_2$

$0.2mg=m{a}_2$

$a_2=2m/s$

Now, displacement of block w.r.t ground is

$s_2=\frac{1}{2}{a}_2{t}^2=\frac{1}{2}\times 2\times 1=1m$ [$t=1s$]

Now, acceleration of block relative to plank is

$a_{BP}=a_2-a_1=2-4=-2m/s^2$

displacement of block relative to plank is

$s=\frac{1}{2}{a}_{BP}{t}^2=\frac{1}{2}\times (-2)\times 1=-1m$