The string between blocks of mass and is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut, find the magnitudes of accelerations of mass and (immediately after cutting). [2006]

Question

The string between blocks of mass $m$ and $2 m$ is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut, find the magnitudes of accelerations of mass $2 m$ and $m$ (immediately after cutting). [2006]

Smart Achievers · Accepted Answer

(3)

Before the string is cut, the tension $T$ has to hold both the masses $2 m$ and $m$ , therefore,

$T = 3 m g$

When the string is cut, the mass $m$ is a freely falling body and its acceleration = acceleration due to gravity = g.

For mass $2 m$ , just after the string is cut, $T$ remains $3 m g$ because of the extension of string.

$∴$ $3 m g - 2 m g = 2 m \cdot a \Rightarrow \frac{g}{2} = a$

Solution

Q.
The string between blocks of mass $m$ and $2 m$ is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut, find the magnitudes of accelerations of mass $2 m$ and $m$ (immediately after cutting). [2006]

1 $g, g$

2 $g, \frac{g}{2}$

3 $\frac{g}{2}, g$

4 $\frac{g}{2}, \frac{g}{2}$

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Solution

Q. The string between blocks of mass m and 2m is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut, find the magnitudes of accelerations of mass 2m and m (immediately after cutting). [2006]

1 g, g

2 g, g2

3 g2, g