Question 1.1: Express the following quantities by using prefixes. (a) 4.0 x 10^-4 m (b) 15.0 x 10^-8 s (c) 7.5 x 10^-7 g

Question 1.2: The length and width of a rectangular plate are (15.6 ± 0.1) cm and (10.80± 0.01) cm respectively. Calculate area of the plate and uncertainty in it.

Question 1.3: The length of a pendulum is (100.0± 0.1) cm. If acceleration of free fall is (9.8 ± 0.1) m/s^2, calculate the percentage uncertainty in time period of the pendulum.

Question 1.4: 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)

Question 1.5: (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= A sin (2πft), where A and f are constants. Find the dimension of A?

Question 1.6: Carry out the following conversions. (a) Calculate the density 1.33 x 10 ^-7 g cm^-3 into kgm^-3. (b) Calculate a speed of 20m/s in km/h.

Question 1.7:  If there are N0= 6.02x 10^23 atoms in 4.0 g of helium, what is the mass of helium atom?

Question 1.8: Compute the following to correct significant digits. (a) 3.85m x 3.9m (b) 1023kg + 8.5489kg (c) 22/7 (d) Mp/me=1.67 x10^ -27 kg/ 9.1096 x10^ -31 kg

Question 1.9: A rectangular metallic piece is 3.70 ± 0.01 cm wide, and (7.20 ± 0.01) cm long. (a)Find the area of the rectangular metallic piece and uncertainty in area. (b) Verify that the sum of the percentage uncertainty in the length and in the width is equal to percentage uncertainty in A.

Question 1.10: Calculate the answer up to appropriate numbers of significant figures. (a) 168.99 x 9 (b) 23.5 + 234.09 (c) 984.25/80.0