Question 1:
easy
A cubical box of wood of side 30 cm weighing 21.6 kg floats on water with two faces horizontal. Calculate the depth of immersion of wood.
Question 2:
easy
Given below are two statements:
Assertion (A): A hydrogen-filled balloon stops rising after it has attained a certain height in the sky.
Reason (R): The atmospheric pressure decreases with height and becomes zero when maximum height is attained by balloon.
As the balloon rises, the density of air decreases, leading to a decrease in buoyant force until it equals the weight of the balloon, so it stops rising. Thus, Assertion is true. However, atmospheric pressure does not become zero at this height, making Reason false.
Question 3:
easy
The atmospheric pressure at a place is \(10^5\text{ Pa}\). If liquid of specific gravity equal to 2, be employed as the barometric liquid, the barometric height will be (\(g = 10\text{ m/s}^2\))
Using the relation \(P = \rho g h\), where density \(\rho = 2 \times 10^3\text{ kg/m}^3\) (specific gravity is 2). Substituting the values: \(10^5 = 2 \times 10^3 \times 10 \times h\). Solving for \(h\) gives \(h = 5\text{ m}\).
Question 4:
easy
Two copper vessels A and B have the same base area but of different shapes. Vessel A takes twice the volume of water as that vessel B requires to fill upto common particular height. Then correct statement among the following is
Liquid pressure at the base depends only on height and density of the liquid, \(P = \rho g h\). Since height is the same, pressure at the base of both vessels is the same.
Question 5:
easy
A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with \(12\text{ cm}\) of water in one arm and \(15\text{ cm}\) of spirit in other. The specific gravity of spirit is
At the interface level, the pressure on both sides must be equal: \(h_w \rho_w g = h_s \rho_s g\). Thus, \(\rho_s / \rho_w = h_w / h_s = 12 / 15 = 0.8\).