Question

Two blocks A and B of mass 2m and 3m respectively are connected by a massless string. The whole system is suspended by a massless spring as shown in figure. The magnitude of acceleration of A and B immediately after the string is cut are respectively​

Answer 1

${\huge{\fcolorbox{black}{PINK}{♡HAN JU HUI♡}}}$

Answer 2

Given:

Two blocks A and B of mass 2m and 3m respectively are connected by a massless string. The whole system is suspended by a massless spring as shown in figure.

To find:

The magnitude of acceleration of A and B immediately after the string is cut are respectively?

Calculation:

In this type of questions, always draw the free body diagram of both the blocks before and after cutting the string.

Diagram 1: Before cutting string

Diagram 2: After cutting string

Before cutting string:

For block A:

$2mg + T = kx \: \: \: .....(1)$

For block B:

$3mg = T \: \: \: \: \: .....(2)$

So, putting value of T :

$\implies \: 2mg + 3mg= kx$

$\implies \: kx = 5mg \: \: \: \: ......(3)$

After cutting string:

For block A:

$2mg - T = 2m(a_{1})$

$\implies \: 2mg - 5mg= 2m(a_{1})$

$\implies \: - 3mg= 2m(a_{1})$

$\implies \: a_{1} = - \dfrac{3g}{2}$

$\boxed{ \implies \: | a_{1}| = \dfrac{3g}{2} }$

For block B:

Block B is falling freely, so it's acceleration will be simply "g".

Hope It Helps.