## Thursday, 18 September 2014

### UNCERTAINITY IN MEASUREMENT PROBLEMS

1.Natalie measures the mass and speed of a glider. The percentage uncertainty in her measurement of the mass is 3% and in the measurement of the speed is 10%. Her calculated value of the kinetic energy of the glider will have an uncertainty of
A.      30%.
B.      23%.
C.      13%.
D.      10%.

2.A student measures a distance several times. The readings lie between 49.8 cm and 50.2 cm. This
measurement is best recorded as
A.      49.8 ± 0.2 cm.
B.      49.8 ± 0.4 cm.
C.      50.0 ± 0.2 cm.
D.      50.0 ± 0.4 cm.

3.The power dissipated in a resistor of resistance R carrying a current I is equal to I2R. The value of I has an uncertainty of ±2% and the value of R has an uncertainty of ±10%. The value of the uncertainty in the calculated power dissipation is
A.      ±8%.
B.      ±12%.
C.      ±14%.
D.      ±20%.
4.Which one of the following is a fundamental unit?
A.      Coulomb
B.      Ohm
C.      Volt
D.      Ampere
5.A student measures two lengths as follows:
T = 10.0 ± 0.1 cm
S = 20.0 ± 0.1 cm.
The student calculates:
FT, the fractional uncertainty in T
FS, the fractional uncertainty in S
FT–S, the fractional uncertainty in (TS)
FT+S, the fractional uncertainty in (T + S).
6.Which of these uncertainties has the largest magnitude?
A.      FT
B.      FS
C.      FT–S
D.      FT+S
7.The volume V of a cylinder of height h and radius r is given by the expression
V = πr2h.
In a particular experiment, r is to be determined from measurements of V and h. The uncertainties in V and in h are as shown below.
 V ± 7% h ± 3%
The approximate uncertainty in r is
A.      10%.
B.      5%.
C.      4%.
D.      2%.
8.The radius of a loop is measured to be (10.0 ± 0.5) cm. Which of the following is the best estimate of the uncertainty in the calculated area of the loop?
A.      0.25%
B.      5%
C.      10%
D.      25%
9.The relationship between two measured quantities P and Q is of the form
P = kQn
where k and n are constants.
A plot of lg P (y-axis) against lg Q (x-axis) will enable the value of k to be determined by measuring only
A.      the intercept on the lg P axis.
B.      the intercept on the lg Q axis.
C.      the slope of the graph.
D.      the reciprocal of the slope of the graph.
10.The volume V of a cylinder of height h and radius r is given by the expression
V = pr2h.
In a particular experiment, r is to be determined from measurements of V and h. The uncertainties in V and in h are as shown below.
 V ±7% h ±3%
The approximate uncertainty in r is
A.      10%.
B.      5%.
C.      4%.
D.      2%.