A submarine experiences a pressure of 5.05 × 10⁶ Pa at a depth of d₁ in a sea. When it goes further to a depth of d₂, it experiences a pressure of 8.08 × 10⁶ Pa. Then d₂ - d₁ is approximately: (density of water = 10³ kg/m³ and acceleration due to gravity = 10 ms^–2)
1.  600 m
2. 400 m
3. 300 m
4. 500 m

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is \(5~\text{cm}\) and the angular speed of rotation is \(\omega\) rads^–1. The difference in the height, \(h~\text{(in cm)}\) of liquid at the centre of vessel and at the side will be:

          
1. \(\dfrac{25 \omega^2}{2 g} \)

2. \( \dfrac{2 \omega^2}{5 g} \)

3. \( \dfrac{5 \omega^2}{2 g} \)

4. \( \dfrac{2 \omega^2}{25 g}\)

A hydraulic press can lift \(100\) kg when a mass \(m\) is placed on the smaller piston. If the diameter of the larger piston is increased by a factor of \(4\) and the diameter of the smaller piston is reduced by a factor of \(4,\) while keeping the same mass \(m\) on the smaller piston, the press can lift:
1. \(2500 ~\text{kg}\)
2. \(50000 ~\text{kg}\)
3. \(25600 ~\text{kg}\)
4. \(550000 ~\text{kg}\)