You are provided with two meter rules and other necessary apparatus.
Place one of the rules on a knife edge and determine its centre of gravity C. Mark this pos with a piece of chalk.
Read and record the mass \(M_R\) of the metre rule written on the reverse side of it.
Attach the mass M= 100g firmly to the rule AB at C using sellotape.
Suspend the metre rule by two parallel threads of length h = 40 cm each at the 10 cm marks. Ensure that the graduated face to the metre rule is facing upwards.
Set the rule AB into a small angular oscillation about the vertical axis through its centre of gravity.
Determine the time, t for 20 complete oscillations. Evaluate the period T and T\(^{2}\)
Read and record the value of d in meters.
Keeping d constant throughout the experiment, repeat the procedure for other values of h = 50, 60, 70, and 80 cm. In each case determine the corresponding values of f T and T. Tabulate your reading. (x) Plot a graph of T on the vertical axis and h on the horizontal axis.
Determine the slope S, of the graph. Evaluate k =s, where Q =2 S, Q 250P
State two precautions taken to ensure accurate results.
(b)i. Define the term couple as it relates to rotational or oscillatory systems.
ii. Give two practical application of a couple in everyday life.
Verified Correct Answer: .
Physical Principles & Numerical Solution
Center of gravity C = 49.5cm
Mass of metre rule (MR) = 135g, d = 80cm = 0.8m
h(cm)
d(m)
t(sec)
T=\(\frac{\text{t(sec)}}{20}\)
T\(^{2}\)(Sec\(^{2}\))
40
0.8
28.0
\(\frac{28.0}{20}\)=1.40
1.9600
50
0.8
29.0
\(\frac{29.0}{20}\)=1.45
2.1025
60
0.8
31.0
\(\frac{31.0}{20}\)=1.55
2.4025
70
0.8
34.0
\(\frac{34.0}{20}\)=1.70
2.8900
80
0.8
37.0
\(\frac{37.0}{20}\)=1.85
3.4225
Slope (s) = \(\frac{\bigtriangleup {T}^{2}}{\bigtriangleup {h(cm)}}\) = \(\frac{(3.42-0.40)sec^{2}}{(80-21)cm}\)
= \(\frac{3.02sec^{2}}{59cm}\)
= 0.0512sec\(^{2}\)cm\(^{-1}\)
K = \(\frac{S}{Q}\), Q = \(\frac{2}{25d^{2}}\)
K = \(\frac {\frac{S}{2}}{25d^{2}}\)
S = 0.0512sec\(^{2}\)cm\(^{-1}\), d = 50cm = 0.8cm
K = \(\frac{0.0512sec^{2}cm^{-1} \times 25 \times (0.80)^{2}}{2}\)
K = \(\frac{0.0512 \times 25 \times 0.6400sec^{2}cm^{-1}}{2}\) = 0.4096sec\(^{2}\)cm\(^{-1}\)m\(^{2}\)
Precautions: i
- ensured smooth and regular oscillations in a horizontal plane.
- ensured there was no error due to parallax when reading my stopwatch.
(b)i. Couple -This can be defined as two forces of the same magnitude acting in opposite directions but not on the same line.
ii. Practical application of couple include:
- Opening or closing taps.
- Turning a spanner.
- Setting a flywheel in motion about an axis through its center
- Motion of a spinning spindle.
- Riding/pedaling of bicycle
Source: Myschool Past Questions Archive (Record #60022)