Question

Two blocks 'A' and 'B' of same mass 'm' attached with a light spring are suspended by a string as shown in figure. Find the acceleration of block 'A' and 'B' just after the string is cut.

Answer 1

R.E.F image

Consider the following F. B. D.

This is the case when the

string is not cut.

Equations that we get are :

$mg-kx=0$

$\Rightarrow kx=mg$

$kx+mg-T=0$

$\Rightarrow 2mg=T$

After the string is just cut.

The tension (T) will become zero but spring force (kx) will remain same as the elongation 'x' has not been altered in such short period of time.

F.B.D after string cut

$kx=mg$

$mg-kx=m{a}_B$

$\Rightarrow 0=a_B$

Also, $mg+kx=m{a}_A$

$\Rightarrow 2mg=m{a}_A$

$\Rightarrow 2g=a_A$

The acceleration of Block 'A' is 2 g

where as acceleration of Block 'B' is 0.