**Problem 1:** Express the given quantities using prefixes.

**Problem 2:** The length and width of a rectangular plate are (15.6±0.1) cm and (10.80 ± 0.01) cm, respectively. Calculate the area of the plate and uncertainty in it.

**Problem 3:** The length of a pendulum is (100 ± 0.1) cm. If the acceleration of the free fall is (9.8 ± 0.1) m/s^{2}, calculate the percentage uncertainty in the time period of the pendulum.

**Problem 4:** Theory suggests that drag force depends upon the viscosity of the medium, average radius of the object and velocity of the object moving through the fluid. Derive a formula for dragging force of fluid by using dimensional analysis. (Hint: viscosity = ML^{-1}T^{-1}).

**Problem 5:** (a) Suppose that the displacement of an object is related to time according to the expression x=Bt^{2}. What are the dimensions of B?

(b) A displacement is related to time as x=Asin(2πft), where A and f are constants. Find the dimensions of A?

**Problem 6:** Carry out the following conversions;

(a) Calculate the density of 1.33 * 10^{-7} g cm^{-3}
into kg m^{-3}.

(b) Calculate a speed of 20 m s^{-1} in km h^{-1}.

**Problem 7:** If there are N_{0} = 6.02 * 10^{23} atoms in 4 gm of helium. What is the mass of one helium atom?

**Problem 8: **Compute the following to correct significant digits.

**Problem 9:** A rectangular metallic piece is (3.7
0.01) cm wide, and (7.20
0.01) cm long.

(a) Find the area of the rectangular metallic piece and uncertainty in the area.

(b) Verify that the sum of the percentage uncertainty in the length and in the width is equal to 0.4%.

**Problem 10:** Calculate the answer up to appropriate number of significant figures.