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A solid sphere of radius R made of a mat...

A solid sphere of radius R made of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless pistion of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid the fractional change in the radius of the sphere, `deltaR//R`, is .............

A

`Mg//2AK`

B

`Mg//3AK`

C

`Mg//AK`

D

`2Mg//3AK`

Text Solution

Verified by Experts

The correct Answer is:
B
Bulk modulus,
`K = ("Stress")/("Volume strain") = (F//A)/(DeltaV//V) = (Mg//A)/(DeltaV//V)`
or `(DeltaV)/(V) = (Mg)/(AK)" "...(i)`
Volume of sphere, `V= (4)/(3) piR^(3)`
`therefore DeltaV = 4piR^(2)DeltaR thereforeR therefore (DeltaV)/(V) = (4piR^(2))/ ((4)/(3) piR^(3)) = 3(DeltaR)/(R)`
or `(Mg)/(Ak) =3 (DeltaR)/(R)`, from (i)
or ` (DeltaR)/(R) = (Mg)/(3AK)" "therefore" " (deltaR)/(R) = (Mg)/(3AK)`
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