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.

Options

• 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

⇒ `"F"_1/"A"_1 = "F"_2/"A"_2`

Case I 

⇒ `"mg"/"A"_1 = (100"g")/"A"_2`        ...(i)

Case II

A'₁ = `"A"_1/16`

A₂ = 16A₂

Now, `("mg"16)/"A"_1 = "Mg"/(16"A"_2)`     ...(ii)

From (i) and (ii), we get

`(16xx100"g")/"A"_2 = "Mg"/(16"A"_2)`

M = 25,600 Kg