Fluid Mechanics

Surface tension is a force per unit length, not force per unit area. The definition of surface tension is the force acting along the surface of a liquid, which tends to minimize the surface area. It is measured in units of force per unit length (N/m). The incorrect statement in the given options is (E), as surface tension is not defined as force per unit area.

The correct option is (E) : Surface tension is a force per unit area

Hydraulic lifts operate on the basis of Pascal’s law, which states that the pressure exerted on an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. In the case of a hydraulic lift, a small force applied on a smaller piston generates a larger force on a larger piston, lifting the load. Pascal's law is fundamental to the design and operation of hydraulic systems, like lifts and presses.

The correct option is (C) : Pascal's law

Step 1: The de Broglie wavelength of a particle is given by , where is Planck's constant, is the mass, and is the velocity of the particle.
Step 2: A decrease in speed by 1% implies .
Step 3: The new wavelength becomes .
Step 4: Thus, the de Broglie wavelength increases by approximately 1%.

Step 1: In a tug-of-war, the force exerted on the rope does not directly determine the winner. Instead, it depends on the force that a person can apply against the ground.
Step 2: The force that allows a person to pull effectively comes from the friction between their feet and the ground. Higher friction provides better resistance, allowing one to pull with greater force.
Step 3: The friction force is given by: where is the coefficient of friction and is the normal force.
Step 4: The person who can exert a larger frictional force will be able to resist the pull of the opponent and apply a stronger opposing force, ultimately winning the game.
Step 5: Therefore, the correct answer is (B). \bigskip