1 Physical Quantities and Units

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      1 Physical Quantities and Units

    Objective Questions 

      1. What are the dimensions of power?

    A ML2T –1

    B MLT–2 

    C ML2T –2

    D ML2T –3 

    2. Which of the following is not equivalent to the unit for energy?

    A Kilowatt-hour (kWh)

    B Newton metre (N m)

    C Watt per second (W s–1)

    D Pressure cubic metre (Pa m3)

    3. The figure shows two forces of 300 N and 400 N acting on a point P.

    The magnitude of the resultant force at P is

    A 437 N

    B 676 N

    C 690 N

    D 700 N

    4. Which of the following experimental techniques reduces the systematic error of the quantitybeing investigated?

    A Adjusting a voltmeter to eliminate its zero error before measuring a voltage.

    B Timing a large number of oscillations to find the period of a simple pendulum.

    C Measuring the external diameter of a test tube repeatedly and calculating the average.

    D Plotting a series of force and extension readings for a spring on a graph, and using it to

    determine the force constant.

    5. Errors in measurement may be either systematic or random.

      Which of the following involves random error?

    A Stopping a digital stopwatch at the end of a race.

    B Using the value of g as 10 N kg–1 when calculating the weight of a mass.

    CNot allowing for zero error on a moving-coil ammeter.D Not subtracting the background count rate when determining the count rate of a radioactive

    source.

    Structured Question 

      1. The resistive force (drag) acting on a vehicle moving in still air is given by

    F  =  Dρ v2

      where  D is the drag coefficient, ρ  is the density of air and v is the velocity of the vehicle.

    (a) (i) Write down the dimensions of F , ρ  and v.

     (ii) Determine the dimensions of  D.

    (b) The value of  D in SI units is 0.2 for a car. At a particular moment, a car that was moving

    with uniform velocity used 4.0 kW of power to overcome the resistance (drag) of the air.

    At what velocity was the car moving if the density of air in SI units is 1.3?

    P20°

    400 N

    300 N

    QB AA STPM Phys V1 C1 4th indd 1QB AA STPM Phys V1 C1 4th.indd 1 3/7/2008 4:56:11 PM3/7/2008 4:56:11 PM

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    Essay Question 

      1. (a) For a fluid flowing through a tube as shown in the figure, the pressure difference at points

    ① and ② is due to two factors:

    • The change in the height of a fluid.

      • Its speed (due to a change in cross-sectional area).

      It can be demonstrated that the pressures are related by

     

     p1 +

    1—2

      2ρ v  1

     + ρ gy1 =  p

    2 +

    1—2

      2ρ v  2

     + ρ gy2

     

    In general,

     p +

    1

    —2  ρ v2

     + ρ gy = constant 

    This is known as Bernoulli’s equation. Perform a check to confirm that it is dimensionally

    consistent.

    (b) Even though the proportionality constants in some relations are dimensionless, many other

    constants found in equations have dimensions. Consider the cases below.

     (i) The minimum velocity needed for an object to escape from the Earth is given by 

    v =2GM ——– R

     

    where  M  is the mass of the Earth and  R is its radius.

    Determine the dimensions of the universal gravitational constant G. What is the unit

    for G in terms of kilogram, metre and second? (ii) The ideal gas equation  pV   = nRT   relates the pressure  p, volume V   and absolute

    temperature T   for n  moles of an ideal gas. Determine the dimensions of the gas

    constant  R.

    v 1

    1

    y 1

      y 2

    2v 2

    QB AA STPM Phys V1 C1 4th indd 2QB AA STPM Phys V1 C1 4th.indd 2 3/7/2008 4:56:12 PM3/7/2008 4:56:12 PM