Question

The acceleration of block B in the figure will be

• A. $\frac { m _ { 2 } g } { \left( 4 m _ { 1 } + m _ { 2 } \right) }$
• B. $\frac { 2 m _ { 2 } g } { \left( 4 m _ { 1 } + m _ { 2 } \right) }$
• C. $\frac { 2 m _ { 1 } g } { \left( m _ { 1 } + 4 m _ { 2 } \right) }$
• D. $\frac { 2 m _ { 1 } g } { \left( m _ { 1 } + m _ { 2 } \right) }$

Answer 1

Answer: (A)

$\frac { m _ { 2 } g } { \left( 4 m _ { 1 } + m _ { 2 } \right) }$

Answer 2

When the block $m _ { 2 }$ moves downward with acceleration a, the acceleration of mass $m _ { 1 }$ will be $m _ { 2 }$.

Let T is the tension in the string.

By drawing the free body diagram of A and B

$T = m _ { 1 } 2 a$ ……..(i)

$m _ { 2 } g - 2 T = m _ { 2 } a$ ……..(ii)

by solving (i) and (ii)

$a = \frac { m _ { 2 } g } { \left( 4 m _ { 1 } + m _ { 2 } \right) }$