NEET Practice Questions (MCQs) with Answers & Solutions

The text explains, 'The pressure $P = F_1/A_1$ is transmitted throughout the liquid to the larger cylinder attached with a larger piston of area $A_2$, which results in an upward force of $P \times A_2$. Therefore, $F_2 = PA_2 = (F_1/A_1)A_2$'. This implies $F_1/A_1 = F_2/A_2$.

The NCERT text states that 'the applied force has been increased by a factor of $A_2/A_1$ and this factor is the mechanical advantage of the device.'

From Example 9.5: $F_1 = 10 N$. $D_1 = 1.0 cm$, $D_2 = 3.0 cm$. Areas are proportional to $D^2$. So, $A_2/A_1 = (D_2/D_1)^2 = (3.0/1.0)^2 = 9$. Since $F_2/A_2 = F_1/A_1$, then $F_2 = F_1 (A_2/A_1) = 10 N \times 9 = 90 N$.

As stated in Example 9.5 (b), 'Water is considered to be perfectly incompressible. Volume covered by the movement of smaller piston inwards is equal to volume moved outwards due to the larger piston.' This means $V_1 = V_2$, or $A_1 L_1 = A_2 L_2$.

From Example 9.6: Force to be lifted ($F_2$) = mass $\times g = 1350 \text{ kg} \times 9.8 \text{ m/s}^2 = 13230 \text{ N}$. Radii are $r_1 = 5.0 \text{ cm}$ and $r_2 = 15 \text{ cm}$. We know $F_1/A_1 = F_2/A_2$, so $F_1 = F_2 (A_1/A_2) = F_2 (\pi r_1^2 / \pi r_2^2) = F_2 (r_1/r_2)^2$. $F_1 = 13230 \text{ N} \times (5/15)^2 = 13230 \text{ N} \times (1/3)^2 = 13230 \text{ N} \times (1/9) = 1470 \text{ N}$.

The text states, 'An important advantage of the system is that the pressure set up by pressing pedal is transmitted equally to all cylinders attached to the four wheels so that the braking effort is equal on all wheels.'

The explanation for Example 9.5 (b) explicitly states, 'Water is considered to be perfectly incompressible. Volume covered by the movement of smaller piston inwards is equal to volume moved outwards due to the larger piston.' This incompressibility is crucial for the efficient and direct transmission of pressure and displacement in hydraulic systems.

The text combines two aspects of Pascal's Law: 'The French scientist Blaise Pascal observed that the pressure in a fluid at rest is the same at all points if they are at the same height.' and 'whenever external pressure is applied on any part of a fluid contained in a vessel, it is transmitted undiminished and equally in all directions.'

The text states: 'It is necessarily the same in all. If we push the piston, the fluid level rises in all the tubes, again reaching the same level in each one of them.' This demonstrates the uniform transmission of pressure.

The text indicates the force is 'increased by a factor of $A_2/A_1$'. If $A_2 = 10 A_1$, then the factor is $10A_1/A_1 = 10$. So, the force is amplified 10 times.