Question 405: Properties of Matter

Question

A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle $	heta$ = 45$^\circ$. P
1
and P
2
are pressures at points 1 and 2, respectively, located at the base of the tube. Let $\beta$ = (P
1
$-$ P
2
)/($ho$gd), where $ho$ is density of water, d is the inner diameter of the tube and g is the acceleration due to gravity. Which of the following statement(s) is(are) correct?
![](https://imagex.cdn.examgoal.net/1kucn7b7o/53677d2f-2606-40ff-af1d-1c8cdaa3a1ba/76c61440-2510-11ec-bb3b-1f67b3a78587/file-1kucn7b7p.png)

Accepted Answer

$({p_1} - {p_2})ds = \rho dsd\sqrt 2 (g\sin 45^\circ  - a)$
$({p_1} - {p_2})ds = \rho d(g - a\sqrt 2 )$
$\beta  = {{({p_1} - {p_2})} \over {\rho gd}} = \left( {1 - {{a\sqrt 2 } \over g}} \right)$
When $a = {g \over {\sqrt 2 }},\beta  = 0$
When $a = {g \over 2},\beta  = \left( {{{\sqrt 2  - 1} \over {\sqrt 2 }}} \right)$

Answer

$\beta$ = 0 when a = g/$\sqrt 2 $

Answer

$\beta$ > 0 when a = g/$\sqrt 2 $

Answer

$\beta  = {{\sqrt 2  - 1} \over {\sqrt 2 }}$ when a = g/2

Answer

$\beta  = {1 \over {\sqrt 2 }}$ when a = g/2

Properties of Matter

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