A student investigates the dimensions of a boiling tube.
The student clamps the boiling tube vertically above a bench and pours a small amount of water to fill the curved bottom of the tube. The initial height of the water level from the bench is h0=3.2 cmh_0 = 3.2\text{ cm}h0=3.2 cm. Suggest one precaution that is taken when measuring this height using a ruler to ensure the reading is accurate.
The student then adds a volume of water V=5.0 cm3V = 5.0\text{ cm}^3V=5.0 cm3 to the tube. The new height of the water level is measured to be h=4.8 cmh = 4.8\text{ cm}h=4.8 cm. Calculate the increase in height H H\,H of the water in the boiling tube using the equation:
H=h−h0 H = h - h_0 H=h−h0The student continues to add water in 5.0 cm3 increments, measuring the height h h\,h each time, and plots a graph of V/ cm3V /\text{ cm}^3V/ cm3 (y-axis) against H/ cmH /\text{ cm}H/ cm (x-axis). The straight line of best fit on the graph passes through the points (1.0,3.1)(1.0, 3.1)(1.0,3.1) and (9.0,28.3)(9.0, 28.3)(9.0,28.3).
Calculate the gradient, GGG, of the line of best fit.
Calculate the inside diameter, DDD, of the boiling tube using the equation:
D=4Gπ D = \sqrt{\frac{4G}{\pi}} D=π4GGive your final answer to 2 significant figures.
Suggest why it is important for the student to add a small amount of water to the boiling tube before taking the initial reading h0h_0h0.
Another student uses this method with the same apparatus to measure D D\,D for a narrow test-tube of diameter approximately 1.1 cm. He adds water in volumes of 1.0 cm3 at a time using a standard measuring cylinder. State and explain one reason why this is not an accurate method for this narrow test-tube.
164 exam-style questions on CIE IGCSE Physics Physical quantities and measurement techniques, covering Physical quantities and measurement techniques. Each one has a worked solution and a mark scheme showing where the marks go.