JEE Advanced 2020 Full Test 2 Paper 1

Area of the piston =π(R2−r2)
Pressure on the base =ρg(H+h) where
ρ= density of water.
Also pressure on the base
=‌

(W+m)g

πR2

∴ρg(H+h)=‌

(W+m)g

πR2

⇒H+h‌

(W+m)

πR2ρ

...........(1)
Considering the equilibrium of the piston Upward thrust = weight of the piston π(R2−r2)‌square‌g‌h=Wg
⇒h=‌

W

π(R2−r2)ρ

..............(2)
From (i) and (ii)
H=‌

W+m

πR2ρ

−‌

W

π(R2−r2)ρ

⇒H=‌

1

πR2ρ

(m−W‌

r2

R2−r2

)
⇒H=‌

1

π×42×10−4×1000

=(0.7−‌

3×12×10−4

(42−12)×10−4

)
=10cm