One joule is equal to how many ergs?

The correct answer is B, joule. Work is the product of force and displacement, so its unit is the newton metre, which is given the name joule; one joule of work is done when a force of one newton moves a body through one metre in its own direction. Energy is measured in the same unit, because work done is energy transferred.

Option A, the newton, is the SI unit of force alone. Option C, the watt, is the unit of power, that is the rate of doing work, and equals one joule per second. Option D, the pascal, is the unit of pressure and equals one newton per square metre. Candidates who confuse the joule with the watt lose marks in the very next question of a paper, so learn the pair as work in joule and power in watt.

The correct answer is C, 90 degrees. Work equals force into displacement into the cosine of the angle between them, and the cosine of ninety degrees is zero, so a force at right angles to the motion does no work at all. This is why the centripetal force in circular motion does no work and why a person carrying a load on the head along a level road does none against gravity.

Option A, zero degrees, gives the maximum positive work, since the cosine of zero is one and force and displacement point the same way. Option B, forty five degrees, gives partial positive work, as the cosine is about 0.707. Option D, 180 degrees, gives the maximum negative work, the case of friction opposing motion. Learning the four cosine values, one, 0.707, zero and minus one, settles this whole family of questions.

The correct answer is B, half of mass into the square of the speed. Kinetic energy is the energy a body has because of its motion, and it grows with the square of the speed, so a body moving twice as fast carries four times the kinetic energy.

Option A is the expression for gravitational potential energy near the surface of the Earth, that is mass into acceleration due to gravity into height, and it depends on position rather than motion. Option C, mass into speed, is the linear momentum of the body, a vector quantity measured in kilogram metre per second, not an energy at all. Option D leaves out the factor of one half and is the standard careless error in this question. Remember also that kinetic energy can be written as the square of momentum divided by twice the mass.

The correct answer is B, watt. Power is the rate of doing work, that is work divided by the time taken, so its unit is the joule per second, which is named the watt after James Watt. A machine of one kilowatt does one thousand joule of work every second.

Option A, the joule, measures work or energy, not the rate at which it is delivered. Option C, the newton second, is the unit of impulse and of momentum. Option D, the kilowatt hour, is a unit of energy in spite of its name, because it is a power multiplied by a time; it is the commercial unit of electricity and equals 3.6 million joule. The confusion between the watt and the kilowatt hour is deliberate in many papers, so keep the distinction of rate against quantity clear.

The correct answer is C, 746 watt. The horsepower is an older unit of power that survives in the rating of motors and vehicles, and one horsepower is taken as about 746 watt, that is roughly three quarters of a kilowatt.

Option A, 100 watt, is close to the rating of an old filament bulb and has no connection with the horsepower. Option B, 500 watt, is simply half a kilowatt and is offered as a plausible round figure. Option D, 1000 watt, is one kilowatt; a common mistake is to treat the horsepower and the kilowatt as equal, when in fact one kilowatt is about 1.34 horsepower. The figure 746 is worth memorising exactly, because the question is often set in reverse, asking how many watt a motor of a given horsepower consumes.