Question

Two balls $A$ and $B$ of masses $100$ gm and $250$ gm respectively are connected by a stretched spring of negligible mass and placed on a smooth table. When the balls are released simultaneously the initial acceleration of $B$ is $10cm/se{c}^2$ westward. What is the magnitude and direction of initial acceleration of the ball $A$

• A. $25cm/s^2$ Eastward
• B. $25cm/s^2$ North ward
• C. $25cm/s^2$ West ward
• D. $25cm/s^2$ South ward

Answer 1

Answer: (A)

$25cm/s^2$ Eastward

The force provided by the spring is internal,
$\overrightarrow{p_s}=constant$
i.e. $m_A\overrightarrow{v_A}+m_B\overrightarrow{v_B}=constant$
$\frac{dt}{dx}(m_A\overrightarrow{v_A}+m_B\overrightarrow{v_B})=0$
or $\overrightarrow{a_A}=-\frac{m_B}{m_A}\overrightarrow{a_B}=-\frac{0.25}{0.10}$ ($10cm/s^2$ west ward)
$=25cm/s^2$ directed east ward
($\because -$ West ward $=$ East ward)