Question

A hollow sphere of radius R is filled completely with an ideal liquid of density p.
Sphere is moving horizontally with an acceleration 2g where g is the acceleration due to gravity at that region.If minimum pressure of liquid is P0 then pressure at the centre of sphere is
a) P0 + pgR
b) P0 +pgRroot 2
c) P0 + pgR root 5
d) P0 +pgR /root 5

Answer 1

Answer:

Pressure at the center of the sphere is given as

$P = P_o + \rho (\sqrt5 g)R$

Explanation:

As we know that Angle of free surface of liquid made with the horizontal is given as

$tan\theta = \frac{a}{g}$

so we will have

$tan\theta = \frac{2g}{g}$

$tan\theta = 2$

now we know that effective gravity on the liquid is given as

$g_{eff} = \sqrt{(2g)^2 + g^2}$

$g_{eff} = \sqrt5 g$

now pressure at the center of the sphere is given as

$P = P_o + \rho g_{eff} R$

$P = P_o + \rho (\sqrt5 g)R$

#Learn

Topic : Fluid pressure

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