Question

A massless, hollow sphere of radius R is entirely filled with a fluid such that its density is p. This same hollow sphere is now compressed so that its radius is R/2, and then it is entirely filled with the same fluid as before. As such, what is the density of the compressed sphere?

a. 8p
b. p/8
c. p/4
d. 4p

Answer 1

a. 8p

Step-by-step explanation:

We are given that

Radius of hollow sphere , R1=R

Density of hollow sphere=
`\rho`

After compress

Radius of hollow sphere, R2=R/2

We have to find density of the compressed sphere.

We know that

`Density=(mass)/(volume)`

`Mass=Density* volume=Constant`

Therefore,
`\rho_1 V_1=\rho_2V_2`

Volume of sphere=
`(4)/(3)\pi r^3`

Using the formula

`\rho* (4)/(3)\pi R^3=\rho_2* (4)/(3)\pi (R/2)^3`

`\rho R^3=\rho_2* (R^3)/(8)`

`\rho_2=8\rho`

Hence, the density of the compressed sphere=
`8\rho`

Option a is correct.