Question

Two masses, $M$ and $m$ are connected together by a pulley two strings and a stretched spring of force constant $k$ as shown. Assume that string, pulley and spring all are massless and surface below $m$ is smooth. The amount by which the spring is stretched is :(assume system moving with constant acceleration)

• A. $\frac{ mMg }{ k ( m + M )}$
• B. $\frac{2 m M g}{k(m+M)}$
• C. $\frac{ Mg }{ k }$
• D. $\frac{( m + M ) g }{2 k }$

Answer 1

Answer: (A)

Acceleration of blocks

$a=\frac{M g}{m+M}$
Tension in the string/spring
$T = ma =\frac{ mMg }{ m + M }$
$\therefore $ Extension in the string, $x =\frac{ T }{ k }$
$=\frac{ mMg }{ k ( m + M )}$