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

a. 8p

Explanation:

We are given that

Radius of hollow sphere , R1=R

Density of hollow sphere=

After compress

Radius of hollow sphere, R2=R/2

We have to find density of the compressed sphere.

We know that

Therefore,

Volume of sphere=

Using the formula

Hence, the density of  the compressed sphere=

Option a is correct.

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