Question

Two balls of mass $1kg$ and $2kg$ respectively are connected to the two ends of the spring. The two balls are pressed together and placed on a smooth table. When released, the lighter ball moves with an acceleration of $2{ms}^{-1}$. The acceleration of the heavier ball will be:

• A. $0.2{ms}^{-2}$
• B. $1{ms}^{-2}$
• C. $2{ms}^{-2}$
• D. $4{ms}^{-2}$

Answer 1

Answer: (B)

$1{ms}^{-2}$

Let $a^{\prime }$ be the acceleration of $2kg$ mass.
for block of mass $1kg$: $a=-kx...\left(1\right)$
for block of mass $2kg$: $2a^{\prime }=-kx..\left(2\right)$
$\left(2\right)/\left(1\right),\frac{2a^{\prime }}{a}=1\Rightarrow a^{\prime }=\frac{a}{2}=\frac{2}{2}=1m/s^2$