Question

1. An experiment is performed in the lab, where the mass and the volume of an object are measured to determine its density. Two completely different valid methods are used. Each experimental method to measure the density is performed, two considerable sets of data are taken on each and the results are compared. The results of the density measurement by each method should be ...

a. dependent on the mass and the volume of the object

b. completely different, because it was measured different ways.

c. correct on the most accurate method and wrong in the other

d. the same within the uncertainty of each measurement method  

2. A sphere and a cylinder have the same volume and radius (R). What is the height of the cylinder, in terms of its radius?

a. 4/3R

b. R

c. none of the above

d. 3/4R

Answer 1

1. Whatever the method followed ( in a valid way ) , the physical quantity will have same measured value within the limit of accuracy of the method.

Error in the experiment depends on the accuracy with which measurements are taken.

So the density of the material will be same within the limit of uncertainty of each measurement

So option ( d ) is correct.

2. Let R be the radius of the sphere and cylinder.

Let h be the height of the cylinder

Volume of the sphere is V = 4/3 * R³

Volume of the cylinder is V' = R² h

Since the volume of the sphere and cylinder are equal ,

V = V'

4/3 * R³ =   R² h

4/3 * R = h

h = 4 R /3

So , height of the cylinder is equal to 4/3 times the radius.