JEE Main20249 Apr 2024Morning ShiftPhysicsMechanical Properties of FluidsActual
A sphere of relative density and diameter D has concentric cavity of diameter d . The ratio of D d , if it just floats on water in a tank is :
Options
- A( -2 +2 )^ 1 / 3
- B( -1 )^ 1 / 3
- C( -1 )^ 1 / 3
- D( +1 -1 )^ 1 / 3
Correct answer
B. ( -1 )^ 1 / 3
Step-by-step solution
weight (w)= 4 3 ( D ^3- d ^3 8 ) g Buoyant force ( F _ b )=1 4 3 ( D ^3 8 ) g For Just Float w = F _ b aligned & (D^3-d^3 ) =D^3 & 1- d^3 D^3 = 1 & 1- 1 = ( d D )^3 & ( -1 )^ 1 3 = ( D d ) aligned