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If the density of a sphere is reduced to...

If the density of a sphere is reduced to `1//8` of its original value, then the radius of the sphere is `"_________"` times its original radius (assume that there is no change in mass). S

A

2

B

4

C

`1//2`

D

`1//4`

Text Solution

Verified by Experts

The correct Answer is:
A
Density `=("mass")/("volume")`
When the density is decreased to `1/8 th ` of its original value, then the volume increases by 8 times the original value.
`v=4/3 pi r^3`
`v_(1)=8v`
`4/3 pi r_(1)^3=8 xx 4/3 pir^3`
`r_(1)^3=8r^3`
`r_(1)=2r`
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