Question

Determine the time in which the smaller block reaches the other end of bigger block in given figure.

• A. 4 $s$
• B. 8 $s$
• C. 2.19 $s$
• D. 3 $s$

Answer 1

The correct option is C 2.19 $s$

Friction between 2 $kg$ block and 8 $kg$ blocks is kinetic in nature, so

$F=\mu \times 2g=0.3\times 2\times 10=6N$
For 2$kg$ block, $10-6=2a_1$
For 8$kg$ block, $6=8a_2\Rightarrow a_{1=}2m{s}^{-2},a_2=\frac{3}{4}m{s}^{-2}$Acceleration of 2$kg$ block relative to 8$kg$ block is
$a_{rel}=a_1-a_2=\frac{5}{4}m{s}^{-2}$
Using the equation of motion, $3=\frac{1}{2}\times \frac{5}{4}{t}^2\Rightarrow t=2.19s$