A spherical tank of 1.2 m radius is half filled with oil of relative density 0.8. If the tank is given a horizontal acceleration of 10 m/s², the maximum pressure at any point on the tank is √2(100−X)100 Pascal. Find the value of X. (g=10 m/s²)
Physics · Mixed Chapter
JEE Mains

Question

A spherical tank of 1.2 m radius is half filled with oil of relative density 0.8. If the tank is given a horizontal acceleration of 10 m/s², the maximum pressure at any point on the tank is √2(100−X)100 Pascal. Find the value of X. (g=10 m/s²)

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: In the tank frame the effective acceleration has magnitude gₑff=√(g²+a²)=√(10²+10²)=10√2 m/s². Step 2: Because the spherical tank is half-filled, the free-surface plane passes through its centre, perpendicular to the effective acceleration. The deepest point is one radius R=1.2 m below that plane. Step 3: Maximum gauge pressure is pₘₐₓ=ρ gₑff R=(0.8×1000)(10√2)(1.2)=9600√2 Pa. Step 4: Compare with √2(100−X)×100: 100−X=96, hence X=4.