Question

A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift ______ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass 'm' on the smaller piston.

विकल्प

• 25400

• 25600

• 25700

• 25800

Answer 1

A hydraulic press can lift 100 kg when a mass 'm' is placed on the smaller piston. It can lift 25600 kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass 'm' on the smaller piston.

Explanation:

Let pressure be P₁ and P₂ and area be A₁ and A₂

So, P₁ = P₂

⇒ ${\displaystyle \frac{{\text{F}}_1}{{\text{A}}_1}=\frac{{\text{F}}_2}{{\text{A}}_2}}$

Case I 

⇒ ${\displaystyle \frac{\text{mg}}{{\text{A}}_1}=\frac{100\text{g}}{{\text{A}}_2}}$        ...(i)

Case II

A'₁ = ${\displaystyle \frac{{\text{A}}_1}{16}}$

A₂ = 16A₂

Now, ${\displaystyle \frac{\text{mg}16}{{\text{A}}_1}=\frac{\text{Mg}}{16{\text{A}}_2}}$     ...(ii)

From (i) and (ii), we get

${\displaystyle \frac{16\times 100\text{g}}{{\text{A}}_2}=\frac{\text{Mg}}{16{\text{A}}_2}}$

M = 25,600 Kg