3 and 4 Marks Question

What is the condition for an object to sink in water? The cross-sectional area of piston A₁ and A₂ is 50cm² and 0.2m² respectively. How many load can lift in piston A₂ if 250N force is applied on piston A₁.
When the density of an object is higher than that of water, the object sinks into water.
Here,
The cross-sectional area of piston A₁ (A₁) = 50 cm² = 0.005 m²
Force applied in piston A₁ (F₁) = 250N
The cross-sectional area of piston A₂
(A₂) = 0.2 m²
Force applied in piston A₂ (F₂) = ?
Now, According to Pascal's law,
Pressure on the small piston = Pressure on the large piston
or, P₁ = P₂
or, $\frac{F_1}{A_1}$ = $\frac{F_2}{A_2}$

or, $\frac{250}{0.005}$ = $\frac{F_2}{0.2}$

∴ F₂ = 10⁴ N.
Study the following diagram and answer the questions.
1. What is the weight of the stone in air?
2. Here,
  weight of the stone in air = weight of the stone in water + weight of water displaced
  = 20 + 5
  = 25N
3. How much upthrust is exerted by water on that stone?
4. Here, upthrust = weight of water displaced
  ∴ upthrust = 5N
5. What is the mass of that stone?
6. We know,
  mass of stone (m) = $\frac{w}{g}$
  = $\frac{25}{10}$
  = 2.5 Kg
An effort of 100N can raise a load of 2000N in a hydraulic press. Calculate the cross-sectional area of a small piston in it. The cross-sectional area of a large piston is 4 m². Write any one applications of Hydraulic press.
Here,
Cross-sectional area of a large piston (A₂) = 4m²
Cross-sectional area of a small piston(A₁) = ?
Effort in small piston (F₁) = 100N
Effort in large piston (F₂) = 2000N
Now, According to Pascal's law,
Pressure on the small piston = Pressure on the large piston
or, P₁ = P₂
or, $\frac{F_1}{A_1}$ = $\frac{F_2}{A_2}$

or, $\frac{100}{A_1}$ = $\frac{2000}{4}$
∴ A₁ = 0.2m²

Hydraulic press is used for compressing cotton, extracting oils from seeds, etc.