Question

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

• A. $a_A=g(\downarrow ),a_B=g(\uparrow )$
• B. $a_A=g(\uparrow ),a_B=g(\downarrow )$
• C. $a_A=\frac{g}{2}(\uparrow )a_B=g(\downarrow )$
• D. $a_A=\frac{3}{2}g(\uparrow ),a_B=\frac{3}{2}g(\downarrow )$

Answer 1

The correct option is B $a_A=g(\uparrow ),a_B=g(\downarrow )$

When string is not cut:
FBD of $A$ block
$kx=mg+T$
FBD of $B$ block
$T=mg$
$\Rightarrow kx=2mg$
When string is cut:
FBD of A block
$kx-mg=m{a}_A$
$2mg-mg=m{a}_A$
$=a_A=g\left(upwards\right)$
FBD of B block
$m{a}_B=mg$
$a_B=g\left(downwards\right)$