A wooden cube of side 10 cm floats at the in | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given: Side of the cube $a = 10 \ cm$, depth in water $x = 3 \ cm$, density of oil $\delta_1 = 0.9 \ g \ cm^{-3}$, density of water $\delta_2 = 1

Vedclass · Accepted Answer

$930$

Vedclass · Answer

(D) Given: Side of the cube $a = 10 \ cm$, depth in water $x = 3 \ cm$, density of oil $\delta_1 = 0.9 \ g \ cm^{-3}$, density of water $\delta_2 = 1 \ g \ cm^{-3}$.Since the cube is floating, the weight of the cube is equal to the total buoyant force exerted by the oil and water.Weight of cube $W = mg$.Buoyant force $F_B = (	ext{Volume in oil} 	imes \delta_1 	imes g) + (	ext{Volume in water} 	imes \delta_2 	imes g)$.Volume of cube $V = a^3 = 10^3 = 1000 \ cm^3$.Volume in water $V_2 = a^2 	imes x = 10^2 	imes 3 = 300 \ cm^3$.Volume in oil $V_1 = a^2 	imes (a - x) = 10^2 	imes (10 - 3) = 700 \ cm^3$.By the law of flotation, $mg = V_1 \delta_1 g + V_2 \delta_2 g$.$m = V_1 \delta_1 + V_2 \delta_2$.$m = (700 	imes 0.9) + (300 	imes 1)$.$m = 630 + 300 = 930 \ g$.

$A$ wooden cube of side $10 \ cm$ floats at the interface between water and oil with its lower surface $3 \ cm$ below the interface. If the density of oil is $0.9 \ g \ cm^{-3}$, the mass of the wooden cube is (in $g$)

Similar Questions

$x$ grams of calcium carbonate was completely burnt in air. The weight of the solid residue formed is $28 \text{ g}$. What is the value of $x$ (in grams)?

In printed scientific names, only the . . . . . . is capitalized.

$A$ magnetized wire of magnetic moment $M$ and length $L$ is bent into an arc of a circle subtending an angle of $60^\circ$ at the center. The new magnetic moment is:

$A$ machine gun fires a bullet of mass $40\, g$ with a velocity $1200\, m/s$. The man holding it can exert a maximum force of $144\, N$ on the gun. How many bullets can he fire per second at the most?

Which of the following methods uses a rotary shaker?

Vedclass Test Series

Exam Paper Generator

Online Exam Module