An astronaut inside a spacecraft orbiting the earth feels weightless because

The correct answer is B, Pascal. Pressure is thrust per unit area, so its unit is one newton per square metre, and this unit is named the pascal after Blaise Pascal. Atmospheric pressure at sea level is about one hundred and one thousand pascals, and the commercial unit bar equals one hundred thousand pascals.

Option A, the newton, is the SI unit of force itself, not of force spread over an area, and it is the numerator in the definition of pressure. Option C, the joule, is the unit of work and energy and equals a newton metre, which is a force multiplied by a distance rather than divided by an area. Option D, the watt, is the unit of power and equals one joule per second. Learn the four together because papers frequently ask which unit goes with which quantity, and pascal, newton, joule and watt appear in the same option set.

The correct answer is B, the poles. The earth is flattened at the poles, so the distance from the centre is least there, and since g varies inversely as the square of that distance, g is largest at the poles. The rotation of the earth also reduces the effective value of g, and that reduction is greatest at the equator and zero at the poles, which adds to the difference.

Option A, the equator, is where g has its smallest surface value, for exactly the opposite reasons. Option C, the centre of the earth, is where g becomes zero, since the mass of the earth then surrounds the body on all sides and its pulls cancel out; a body there has weight zero although its mass is unchanged. Option D, the top of Mount Everest, is far above sea level, and g decreases with height, so it is smaller there than at sea level. The order worth remembering is poles greatest, equator smaller, height smaller still, centre zero.

The correct answer is C, 11.2 kilometres per second. Escape velocity is the minimum speed a body must be given so that it leaves the gravitational pull of the planet and never returns. It depends only on the mass and radius of the planet and not on the mass of the body projected or on the direction of projection, and for the earth it works out at about 11.2 kilometres per second.

Option A, about 7.9 kilometres per second, is the orbital velocity for a satellite close to the earth's surface, and it is smaller than the escape velocity by a factor of the square root of two. Option B, 9.8, is the numerical value of the acceleration due to gravity in metres per second squared and has nothing to do with escape velocity except as a familiar number. Option D is far too large for the earth. The moon's escape velocity is only about 2.4 kilometres per second, which is why it cannot retain an atmosphere.

The correct answer is B, Pascal's law. Pascal's law states that pressure applied to an enclosed fluid is transmitted undiminished in every direction to all parts of the fluid and to the walls of the container. In a hydraulic brake a small force on the narrow master piston creates a pressure that reaches the wider pistons at the wheels, where the same pressure over a larger area gives a much larger force, and all wheels are braked equally at the same moment.

Option A, Archimedes' principle, deals with the upward buoyant force on a body immersed in a fluid and explains ships, submarines and the lactometer. Option C, Bernoulli's principle, relates the speed of a flowing fluid to its pressure and explains the lift of an aerofoil and the working of an atomiser. Option D, Newton's law of gravitation, concerns the attraction between masses. The hydraulic lift and the hydraulic press are the other two standard applications of Pascal's law.

The correct answer is B, Archimedes' principle. It states that a body immersed wholly or partly in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced, so the apparent loss in weight of the body equals the weight of the displaced fluid. A body floats when the weight of fluid displaced equals its own weight, which is the law of flotation, and the same idea explains the ship, the submarine, the hydrometer and the lactometer.

Option A, Pascal's law, deals with the transmission of pressure through an enclosed fluid and explains hydraulic machines. Option C, Hooke's law, is about elasticity and states that within the elastic limit stress is proportional to strain. Option D, Boyle's law, is a gas law stating that at constant temperature the pressure of a fixed mass of gas is inversely proportional to its volume. The two fluid laws, Pascal and Archimedes, are the ones most often swapped in objective papers.