IIT-JEE 2007 · Paper 2 · Physics Q5

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PhysicsSingle correct+3 / -1Question 5 of 66

Water is filled up to a height $h$ in a beaker of radius $R$ as shown in the figure. The density of water is $\rho$ , the surface tension of water is $T$ and the atmospheric pressure is $P_0$ . Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

A cylindrical beaker of diameter 2R containing water to height h; a vertical rectangular section ABCD through a diameter of the water column (AB along the water surface, CD along the bottom).

\left|2P_0Rh+\pi R^2\rho gh-2RT\right|

\left|2P_0Rh+R\rho gh^2-2RT\right|

\left|P_0\pi R^2+R\rho gh^2-2RT\right|

\left|P_0\pi R^2+R\rho gh^2+2RT\right|

Answer and worked solution

Official answer: B

Pressure on the section. ABCD is a rectangle of width $2R$ and height $h$ . At depth $y$ the pressure is $P_0+\rho gy$ , so the water on one side pushes on the other with
$\int_0^h(P_0+\rho gy)\,2R\,dy=2P_0Rh+R\rho gh^2.$

Surface tension. Along the line AB (length $2R$ ) on the free surface, each half pulls the other with $T\cdot2R$ , opposite to the pressure push.

Net force. $\left|2P_0Rh+R\rho gh^2-2RT\right|$ .

(B)

Topics:Surface tension Pressure and Pascal's law

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IIT-JEE 2007 · Paper 2, Physics question 5