Final answer:
To determine the force required to support the object on piston 2, we can use Pascal's principle. According to Pascal's principle, the ratio of the force on piston 1 to the force on piston 2 is equal to the ratio of the areas of the two pistons.
Step-by-step explanation:
To determine the force required to support the object on piston 2, we can use Pascal's principle. According to Pascal's principle, the ratio of the force on piston 1 to the force on piston 2 is equal to the ratio of the areas of the two pistons. Using the formula:
F₁/F₂ = A₁/A₂
We can rearrange the formula to solve for the force on piston 1:
F₁ = (A₁/A₂) x F₂
Given that the diameter of piston 2 is 9.76 cm, we can calculate its radius (r) by dividing the diameter by 2:
r = 9.76 cm / 2 = 4.88 cm = 0.0488 m
Since the height difference is neglected and the pistons are assumed to be massless, we can assume that the object's weight is evenly distributed on piston 2. Therefore, the force on piston 2 (F₂) is equal to the weight of the object:
F₂ = m x g
where m is the mass of the object and g is the acceleration due to gravity.