Question

Mass of upper block and lower block kept over the table is $2kg$ and $1kg$ respectively and coefficient of friction between the blocks is $0.1$. Table surface is smooth. The maximum mass $m$ for which all the three blocks move with same acceleration is $(g=10m/s^2)$

• A. $1kg$
• B. $2/3kg$
• C. $1/3kg$
• D. $3/4kg$

Answer 1

The correct option is D $3/4kg$

Drawing FBDs and writing force equations,

$T-f_r=2a$
$f_{12}=\mu \times 2g=0.1\times 2\times 10=2N$
$\Rightarrow T-2=2a--\left(1\right)$

$f_{12}=1.a=2--\left(2\right)$
$\Rightarrow a=2m/s^2$
$\Rightarrow T=3a=3\times 2=6N$

$mg-T=ma$
$mg-6=m\times 2$
$10m-2m=6$
$8m=6$
$\Rightarrow m=6/8=3/4kg$