Question

Find the acceleration ( in ${\text{m/s}}^2$) of $2\text{kg}$ block in the figures $\left(A\right)$ and $\left(B\right)$ shown at the instant when $1\text{kg}$ block falls from $2\text{kg}$ block (at $t=0$). (Systems are in equilibrium at $t=0$)
(Take $g=10m/s^2$)

• A. $0,0$
• B. $0,5$
• C. $5,5$
• D. $5,0$

Answer 1

The correct option is D $5,0$

F.B.D.s before fall of $1\text{kg}$ block

After the fall of the $1\text{kg}$ block, tension will change instantaneously but spring force $\left(kx\right)$ doesn’t change instantaneously. F.B.D's just after the fall of $1\text{kg}$ block.

Acceleration, $a=\frac{\text{Net force}}{\text{Mass}}$
$a_A=\frac{30-20}{2}=5{\text{m/s}}^2$ (upward)
$a_B=\frac{20-20}{2}=0{\text{m/s}}^2$