In a $U-$tube experiment,a column $AB$ of water is balanced by a column $CD$ of oil,as shown in the figure. Then the relative density of oil is

  • A
    $\frac{h_2}{h_1}$
  • B
    $\frac{h_1}{h_2}$
  • C
    $\frac{h_1 - h_2}{h_1}$
  • D
    $\frac{h_2}{h_1 + h_2}$

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$A$ litre of alcohol weighs

Fill in the blanks:
$(i)$ $1 \text{ atm} = \dots \text{ Pascal}$
$(ii)$ $1 \text{ torr} = \dots \text{ Pascal}$
$(iii)$ $1 \text{ bar} = \dots \text{ Pa}$
$(iv)$ $1 \text{ atm} = \dots \text{ cm Hg}$

The figure shows a container filled with a liquid of density $\rho$. Four points $A, B, C$ and $D$ lie on the diametrically opposite points of a circle as shown. Points $A$ and $C$ lie on a vertical line,and points $B$ and $D$ lie on a horizontal line. Which of the following statements is incorrect? (Here,$p_A, p_B, p_C, p_D$ are the absolute pressures at the respective points.)

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Explain why:
$(a)$ The blood pressure in humans is greater at the feet than at the brain.
$(b)$ Atmospheric pressure at a height of about $6 \; km$ decreases to nearly half of its value at sea level,though the height of the atmosphere is more than $100 \; km$.
$(c)$ Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.

Two immiscible liquids $A$ and $B$ are kept in an $U$-tube. If the density of liquid $A$ is smaller than the density of liquid $B$,then the equilibrium situation is

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