Answer :
Answer:
F₁ = 100 N
Explanation:
The pressure must be equally transmitted from the piston to the narrow arm. Therefore,
P₁ = P₂
F₁/A₁ = F₂/A₂
F₁/F₂ = A₁/A₂
where,
F₁ = Force Required to be applied to piston = ?
F₂ = Force to push cork at narrow arm = 16 N
A₁ = Area of wider arm = πd₁²/4
A₂ = Area of narrow arm = πd₂²/4
Therefore,
F₁/16 N = (πd₁²/4)/(πd₂²/4)
F₁ = (16 N)(d₁²/d₂²)
but, it is given that the diameter of wider arm is 2.5 times the diameter of the narrow arm.
d₁ = 2.5 d₂
Therefore,
F₁ = (16 N)[(2.5 d₂)²/d₂²]
F₁ = (16 N)(6.25)
F₁ = 100 N