## Numerical Problems on Measurement, Physics 11

See here solved numerical problems on Measurement (new course) included in the Physics course for First Year students.

 S No. Statement of problem Problem 1 A circular pizza into 3 equal parts, one piece of pizza is taken out. Estimate the degree measure of the single piece of pizza and convert the measure into radians. What is the radian measure of the angle of the remaining part of pizza?See Solution Problem 2 The length of a a pendulum is (1.5 ± 0.01) m and the acceleration due to gravity is taken to be (9.8 ± 0.1) ms-2. Calculate the time period of the pendulum with uncertainty in it.See Solution Problem 3 Determine the area of a rectangular sheet with length (l ± Δl) = (1.50 ± 0.02) m and width (w ± Δw) = (0.20 ± 0.01) m. Calculate the area (A ± ΔA).See Solution Problem 4 Calculate the answer up to appropriate numbers of significant digits:(a) 246.24 + 238.278 + 98.3 (b) (1.4 × 2.639) + 117.25(c) (2.66 × 104) – (1.03 × 103) (d) (112 × 0.456)/(3.2 × 120)(e) 168.99 × 9 (f) 1023 + 8.5489See Solution Problem 5 Question 5: Calculate the answer up to appropriate numbers of significant digits.See Solution Problem 6 Question 6: Find the dimensions ofPlanck’s constant ‘h’ from formula E = hf, where E is energy and f is frequency.Gravitational constant ‘G’ from the formula F=G (m_1 m_2)/r^2 where F is force m1 and m2 are masses of the objects and ‘r’ is the distance between the centers of the objects.See Solution Problem 7 Question 7: Show that (a) KE = ½ mv2 (b) PEg = mghSee Solution

## Assignments from the text

Assignment 1.1

A pulley of radius 0.9 m is used to lift a bucket from the well. If it took 3.6 rotations for the pulley to take water out of the well, how deep is water in the well?
Solution

Assignment 1.2

A physicist calculated the wall width of half brick thickness (the brick is laid in a flat position, lengthwise called stretcher position), as (13.6 ± 0.1) cm. And one brick thickness (the brick is placed in flat position, lengthwise orthogonal to wall, called header position), as (23.6 ± 0.1) cm. Calculate difference in width of walls with uncertainty in it.

Solution

Assignment 1.3

The voltage V(V ± ΔV) is measured (7.3 V ± 0.1V) and current I(I ± ΔI) is measured as (2.73 A ± 0.05 A). Calculate the resistance R by using Ohm’s law as R = V/I.

Solution

Assignment 1.5

Calculate the answer to the appropriate number of significant figures.

• 31 + 0.1        (b) 658.0 + 23.5478 + 1345.29      (c) 8 × 7

(d) 0.9935 × 10.48 × 13.4 (e) 5.5/1.1                                  (f) (73.2 + 18.72 × 6.1)/3.4

Solution

Assignment 1.6

Show that the equations                              (a) vf = vi + at                      (b) S = vit + ½ at2         are dimensionally correct.

Solution

Assignment 1.7

Find an expression for the time period ‘T’ of a simple pendulum. The time period ‘T’ may depend upon (i) mass ‘m’ of the bob of the pendulum, (ii) length ‘l’ of pendulum, (iii) acceleration due to gravity ‘g’ at the place where the pendulum is suspended.

Solution