A large cylindrical vessel contains water to a height of $10 m$ . It is found that the thrust acting on the curved surface is equal to that at the bottom. if atmospheric pressure can support a water column of $10 m,$ the radius of the vessel is :

10 m

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15 m

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5 m

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25 m

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Solution

The correct option is C $15 m$
Thrust on the curved surface

$= 2 π R h (P_{0} + \frac{h}{2}) = 300 π R$

whereas the thrust on the bottom

$= π R^{2} (P_{0} + h) = 20 π R^{2}$ .

The atmospheric pressure in terms of the column of water is 10 m.

Equating the two thrusts gives

$R = 15 m .$

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A large cylindrical vessel contains water to a height of 10m. It is found that the thrust acting on the curved surface is equal to that at the bottom. if atmospheric pressure can support a water column of 10m, the radius of the vessel is :

The correct option is C 15mThrust on the curved surface =2πRh(P0+h2)=300πRwhereas the thrust on the bottom =πR2(P0+h)=20πR2 . The atmospheric pressure in terms of the column of water is 10 m. Equating the two thrusts gives R=15m.

A large cylindrical vessel contains water to a height of $10 m$ . It is found that the thrust acting on the curved surface is equal to that at the bottom. if atmospheric pressure can support a water column of $10 m,$ the radius of the vessel is :

The correct option is C $15 m$
Thrust on the curved surface

$= 2 π R h (P_{0} + \frac{h}{2}) = 300 π R$

whereas the thrust on the bottom

$= π R^{2} (P_{0} + h) = 20 π R^{2}$ .

The atmospheric pressure in terms of the column of water is 10 m.

Equating the two thrusts gives

$R = 15 m .$