First slide

Pressure in a fluid-mechanical properties of fluids

Question

In the arrangement as shown $m_{B} = 3 M$ , density of liquid is $ρ$ and density of block B is $2 ρ$ . The system is released from rest so that block B moves up when in liquid and moves down when out of liquid with the same acceleration. The mass of block A is

Difficult

A

$\frac{7}{4} M$
B

2 M
C

$\frac{9}{2} M$
D

$\frac{9}{4} M$

Solution

Acceleration when block B is in liquid $a_{1} = \frac{m_{A} g - (m_{B} g - u p t h r u s t)}{m_{A} + 3 m}$
                                                                                      $= \frac{m_{A} g - (3 m g - \frac{3 m}{2 ρ} ρ g)}{m_{A} + 3 m} (↑)$

                    Acceleration when block B is outside the liquid is $a_{2} = \frac{3 m g - m_{A} g}{m_{A} + 3 m} (↓)$

                    Given $a_{1} = a_{2}$

                    $m_{A} g - \frac{3}{2} m g = 3 m g - m_{A} g$

                    $2 m_{A} g = \frac{9}{2} m g$

                $m_{A} = (\frac{9}{4}) m$

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