Answer the following problem. Number 6, 7, and 8 only! Show the solution.

Homework #2 (Uncertainty and Error Analysis) 3. The mass of an object is found to be (24.5 i 0.1) 3. Find the (a) absolute certainty and (b) relative uncertainty of the mass of the object. 4. The density of an object was found to be 2.73%; i 1.2%. What is the absolute uncertainty of the density of the object? 5. The following are the values obtained in measuring the temperature of a room: 310C, 30.5C, 30.0C, 31.3C, 30.8C, 306C, and 31.1%\". What is the room temperature? 6. The length of a pencil was measured using a ruler (shown in the figure). *7\" " ' Wm Find (a) the best estimate of the length of the pencil, (b) the least count of the ruler, (c) the length of the pencil when expressed in terms of 1 cm absolute uncertainty, and (d) the length of the pencil when expressed in terms of relative uncertainty / \"nan-3hr: err: ...,. . .. .. . . . /.. . Homework #2 (Uncertainty and Error Analysis) 7. Find the circumference and cross-sectional area of a circle with radius (3.25 i 0.01) cm. 8. A cylindrical object has a density of (2.7 i 0.3) g/cm3. What is the mass of this object if its radius and height are (2.5 i 0.1) cm and (6.75 i 0.05) cm, respectively? 9. Ohm's law states that V = IR where V is the voltage in volts (V), I is the current in amperes (A), and R is the resistance in ohm (0.). In an experiment to verify Ohm's Law, the resistance of a circuit is increased from 1.0 0 to 10.0 0 and the corresponding current is recorded at a constant voltage 20.0 V. The table below shows the results of this experiment