An arrangement of spring, strings, pulley and masses is shown in figure below.pulley and strings are

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4-1.Newton's Laws of Motion

normal

An arrangement of spring, strings, pulley and masses is shown in the figure below.The pulley and the strings are massless and $M>m$. The spring is light with spring constant $k$. If the string connecting $m$ to the ground is detached, then immediately after detachment

Athe magnitude of the acceleration of $m$ is zero and that of $M$ is $g$

Bthe magnitude of the acceleration of $m$ is $(M-m) g / m$ and that of $M$ is zero

Cthe accelerations of both masses are same

Dthe elongation in the spring is $(M-m) \,g / k$

(KVPY-2018)

Solution

$(b)$ At $t=0, T=m g$
When string is cut, mass $M$ remains static and spring snaps. For mass $m$ at the instant string is cut, forces on $m$ are
Accelcration of $m$ is upwards as spring snaps,
$a_{m}=\frac{F_{\text {net }}}{m}=\frac{M g-m g}{m}$
$=\left(\frac{M-m}{m}\right) g$

Standard 11

Physics

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