The angle which the free surface of a liquid filled in a container will make with horizontal if the container is accelerated horizontally with acceleration g√3 is
Question
The angle which the free surface of a liquid filled in a container will make with horizontal if the container is accelerated horizontally with acceleration g√3 is
Solution
The angle which the free surface of a liquid filled in a container will make with the horizontal if the container is accelerated horizontally with acceleration g√3 can be found using the concept of pseudo force in a non-inertial frame of reference.
Step 1: Understand the situation When the container is accelerated, the liquid inside it experiences a pseudo force in the opposite direction. This force causes the liquid to tilt, forming an angle with the horizontal.
Step 2: Apply the concept of pseudo force The pseudo force acting on the liquid is equal to the mass of the liquid times the acceleration of the container, which is g√3. This force acts in the opposite direction of the acceleration.
Step 3: Find the angle The angle θ that the free surface of the liquid makes with the horizontal can be found using the equation tanθ = a/g, where a is the acceleration of the container and g is the acceleration due to gravity.
So, tanθ = g√3 / g = √3
Therefore, θ = tan^-1(√3) = 60 degrees.
So, the free surface of the liquid will make an angle of 60 degrees with the horizontal.
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