Question

A hemispherical vessel of mass 10^3kg and radius r = 1m is completely filled with a liquid of mass 2×10^3 kg .The height of centre of mass of the system from the ground is?
Answer with explanation
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Answer 1

Answer:

Explanation:

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Answer 2

Answer:

The height of center of mass of the system from the ground is 0.583 m.

Explanation:

Given that,

Mass of vessel $m=10^3\ kg$

Radius r = 1 m

Mass of liquid $m'=2\times10^{3}\ kg$

For hemispherical vessel

$y_{1}=\dfrac{r}{2}$

$y_{1}=\dfrac{1}{2}$

For hemispherical liquid

$y_{2}=r-\dfrac{r}{8}$

$y_{2}=\dfrac{5r}{8}$

$y_{2}=\dfrac{5}{8}$

The height of center of mass of the system from the ground is

$y_{cm}=\dfrac{m_{1}y_{1}+m_{2}y_{2}}{m_{1}+m_{2}}$

$y_{cm}=\dfrac{10^3\times \dfrac{1}{2}+2\times 10^{3}\times\dfrac{5}{8}}{10^{3}+2\times10^{3}}$

$y_{cm}=\dfrac{7}{12}=0.583\ m$

Hence, The height of center of mass of the system from the ground is 0.583 m.