Fluid Mechanics Viscosity Question 277
Question: In the arrangement as shown,$ m_{B}=3m $ , density of liquid is r and density of block B is v. 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. Find the mass of block A.
Options:
A) $ \frac{7}{4}m $
B) $ 2m $
C) $ \frac{9}{2}m $
D) $ \frac{9}{4}m $
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Answer:
Correct Answer: D
Solution:
[d] Acceleration when block B is in the liquid $ a_{1}=\frac{m_{A}g-(m_{B}g-upthrust)}{(m_{A}+3m)} $ $ =\frac{m_{A}g-\left( 3mg-\frac{3m}{2\rho }\rho g \right)}{(m_{A}+3m)}\uparrow $ Acceleration when block B is outside if the liquid, $ a_{2}=\frac{3mg-m_{A}g}{(m_{A}+3m)}(\downarrow ) $ $ Given,a_{1}=a_{2} $ , we get $ m_{A}g-\frac{3}{2}mg=3mg-m_{A}g $ $ \Rightarrow ,,,2m_{A}g-\frac{9}{2}mg\Rightarrow m_{A}=\left( \frac{9}{4} \right)m $
BETA
