3 and 4 Marks Question

What is the condition for an object to sink in water? The crosssectional
area of piston A_{1} and A_{2} is 50cm^{2} and
0.2m^{2} respectively. How many load can lift in piston A_{2}
if 250N force is applied on piston A_{1}.

When the density of an object is higher than that of water, the object sinks
into water.
Here,
The crosssectional area of piston A_{1} (A_{1}) = 50 cm^{2} = 0.005 m^{2}
Force applied in piston A_{1} (F_{1}) = 250N
The crosssectional area of piston A_{2}
(A_{2}) = 0.2 m^{2}
Force applied in piston A_{2} (F_{2}) = ?Now, According to Pascal's law,
Pressure on the small piston = Pressure on the large piston
or, P_{1} = P_{2}
or, $\frac{F_1}{A_1}$ = $\frac{F_2}{A_2}$
or, $\frac{250}{0.005}$ = $\frac{F_2}{0.2}$
∴ F_{2} = 10^{4} N. 
Study the following diagram and answer the questions.

 What is the weight of the stone in air?

Here,
weight of the stone in air = weight of the stone in water + weight of water displaced
= 20 + 5
= 25N  How much upthrust is exerted by water on that stone?

Here, upthrust = weight of water displaced
∴ upthrust = 5N  What is the mass of that stone?

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 crosssectional area of a small piston in it. The crosssectional area of a large piston is 4 m^{2}. Write any one applications of Hydraulic press.

Here,
Crosssectional area of a large piston (A_{2}) = 4m^{2}
Crosssectional area of a small piston(A_{1}) = ?
Effort in small piston (F_{1}) = 100N
Effort in large piston (F_{2}) = 2000NNow, According to Pascal's law,
Pressure on the small piston = Pressure on the large piston
or, P_{1} = P_{2}
or, $\frac{F_1}{A_1}$ = $\frac{F_2}{A_2}$
or, $\frac{100}{A_1}$ = $\frac{2000}{4}$
∴ A_{1} = 0.2m^{2}Hydraulic press is used for compressing cotton, extracting oils from seeds, etc.