An ice cube of edge 1 cm melts in a gravity- | vedclass

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

Question

(A) Given,edge of the cube $x = 1 \ cm$. Volume of the cube $V = x^3 = (1 \ cm)^3 = 1 \ cm^3$. Since the ice melts in a gravity-free container,the wat

Vedclass · Accepted Answer

$(36 \pi)^{1/3} \ cm^2$

Vedclass · Answer

(A) Given,edge of the cube $x = 1 \ cm$. Volume of the cube $V = x^3 = (1 \ cm)^3 = 1 \ cm^3$. Since the ice melts in a gravity-free container,the water forms a spherical drop. Volume of the spherical drop = Volume of the cube = $1 \ cm^3$. Let $r$ be the radius of the spherical drop. $\frac{4}{3} \pi r^3 = 1 \implies r^3 = \frac{3}{4 \pi} \implies r = \left(\frac{3}{4 \pi}ight)^{1/3}$. Surface area of the spherical drop $A = 4 \pi r^2$. $A = 4 \pi \left(\frac{3}{4 \pi}ight)^{2/3} = 4 \pi \frac{3^{2/3}}{(4 \pi)^{2/3}}$. $A = (4 \pi)^{1 - 2/3} 	imes 3^{2/3} 	imes 4^{2/3} / 4^{2/3} 	ext{ (simplifying powers)} = (4 \pi)^{1/3} 	imes (3^2)^{1/3} = (4 \pi 	imes 9)^{1/3} = (36 \pi)^{1/3} \ cm^2$.

An ice cube of edge $1 \ cm$ melts in a gravity-free container. The approximate surface area of the water formed is (water is in the form of a spherical drop)

Similar Questions

Fill in the blanks:
$(i)$ $A$ bubble in water has .......... free surface.
$(ii)$ $A$ bubble in air has .......... free surface.
$(iii)$ $A$ rain drop has .......... free surface.

The excess pressure inside a soap bubble $A$ in air is half the excess pressure inside another soap bubble $B$ in air. If the volume of the bubble $A$ is $n$ times the volume of the bubble $B$,then the value of $n$ is . . . . . . .

$A$ spherical liquid drop splits into $729$ identical spherical drops. If $E$ is the surface energy of the original drop and $U$ is the total surface energy of the resulting drops,then $\frac{E}{U} = \frac{1}{x}$. The value of $x$ is

The excess pressure inside a spherical drop of water is three times that of another drop of water. The ratio of their surface area is

The pressure inside two soap bubbles, $A$ and $B$, is $1.01 \,atm$ and $1.02 \,atm$ respectively. The ratio of their respective radii $(r_A : r_B)$ is (outside pressure $= 1 \,atm$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module