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 $10m/s^2$, the maximum pressure on the tank is $\sqrt{2}P$ pascal. Find the value of P:

Answer 1

The angle made by surface of the oil with horizontal is give as, $tan\theta =g/a=10/10=1\Rightarrow \theta ={45}^o$

Refer the figure attached, It can be noticed that the maximum depth is $MT=2rsin\theta$

So, maximum pressure $P=\rho g\times \left(2rsin\theta \right)=800\times 10\times 2.4sin{45}^o=9600\sqrt{2}$

$\Rightarrow P\sqrt{2}=9600\sqrt{2}\Rightarrow P=9600pascal$.