Part(A)

Buoyant force will equal for both

 

Part(B)

No

Step-by-step explanation

Part(A)

 

Let both sphere are dip into the fluid having density ?ρL??

 

Let volume of both sphere (having same diameter) is V

 

Therefore,

Buoyancy force on lead sphere is ?FBL?=ρL?Vg?

 

Buoyancy force on aluminium sphere is ?FBA?=ρL?Vg?

 

From above equations we can say that :

 

?FBL?=FBA??

 

So, buoyant force on both sphere is same

 

Because for both liquid liquid is same

 

 

Part(B)

No, answer in the part(A) doesn't depends on the fluid

 

Because if fluid is same for both sphere then buoyancy force on both sphere will be same

 

If we change the fluid then buoyancy force of each sphere will change.

 

For example :

 

Case:1

 

Let both sphere are dip into the fluid having density ?ρL??

 

Let volume of both sphere (having same diameter) is V

 

Therefore,

Buoyancy force on lead sphere is ?FBL?=ρL?Vg?

 

Buoyancy force on aluminium sphere is ?FBA?=ρL?Vg?

 

From above equations we can say that :

 

?FBL?=FBA??

 

Case :2

 

Let change the fluid having different density

 

Let density of fluid is D

Volume of sphere is V

 

Therefore,

 

Buoyancy force on lead sphere is ?FBL?=DVg?

 

Buoyancy force on aluminium sphere is ?FBA?=DVg?

 

Again

 

?FBL?=FBA??