Two spheres made of the same substance have d | vedclass

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

Question

(B) The thermal capacity $C$ of an object is defined as the product of its mass $m$ and its specific heat capacity $S$,given by $C = mS$.Since the sph

Vedclass · Accepted Answer

$1: 8$

Vedclass · Answer

(B) The thermal capacity $C$ of an object is defined as the product of its mass $m$ and its specific heat capacity $S$,given by $C = mS$.Since the spheres are made of the same substance,they have the same density $ho$ and the same specific heat capacity $S$.The mass of a sphere is given by $m = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi r^3 ho$.Therefore,the thermal capacity is $C = \left( \frac{4}{3} \pi r^3 ho ight) S$.Since $\frac{4}{3}$,$\pi$,$ho$,and $S$ are constants,the thermal capacity is proportional to the cube of the radius,$C \propto r^3$.Given the ratio of diameters is $1: 2$,the ratio of radii $r_1 : r_2$ is also $1: 2$.The ratio of thermal capacities is $\frac{C_1}{C_2} = \left( \frac{r_1}{r_2} ight)^3 = \left( \frac{1}{2} ight)^3 = \frac{1}{8}$.Thus,the ratio is $1: 8$.

Two spheres made of the same substance have diameters in the ratio $1: 2$. Their thermal capacities are in the ratio of .............

Similar Questions

Which of the following organisms possesses a cell wall?

The value of $x$,where $x>0$ and $\tan \left(\sec ^{-1}\left(\frac{1}{x}\right)\right)=\sin \left(\tan ^{-1} 2\right)$ is

Who among the following is known as the 'Father of Taxonomy'?

Aluminium reacts with $NaOH$ and forms compound '$X$'. If the coordination number of aluminium in '$X$' is $6$,the correct formula of $X$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module