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?

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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