# Chapter 2 – Units and Measurements Questions and Answers: NCERT Solutions for Class 11 Physics

Class 11 Physics NCERT book solutions for Chapter 2 - Units and Measurements Questions and Answers. ## Question 2. 2. Fill in the blanks by suitable conversion of units (a) 1 kg m2 s-2= …. g cm2s-2 (b) 1 m =………… ly (c) 3.0 m s-2= …. kmh-2 (d) G = 6.67 x 10-11N m2(kg)-2= …. (cm)3s-2g-1. ## Question 2. 3. A calorie is a unit of heat or energy and it equals about 4.2 J where 1 J = 1 kgm2s-2. Suppose we employ a system of units in which the unit of mass equals a kg, the unit of length equals j8 m, the. unit of time is ys. Show that a calorie has a magnitude 4.2α-1 β-2 γ2in terms of the new units.  ## Question 2. 9. The photograph of a house occupies an area of 1.75 cm2on a 35 mm slide. The slide is projected on to a screen, and the area of the house on the screen is 1.55 m2. What is the linear magnification of the projector-screen arrangement?

### Answer:Here area of the house on slide = 1.75 cm2= 1.75 x 10-4m2and area of the house of projector-screen = 1.55 m2 .•. Areal magnification =Area on screen/Area on slide = 1.55 m2/ 1.75 x 10-4m2= 8.857 x 103 .•. Linear magnification ## Question 2. 13. A physical quantity P is related to four observables a, b, c and d as follows: ## The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result? ## Question 2. 14. A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion: ## (a = maximum displacement of the particle, v = speed of the particle, T = time-period of motion)Rule out the wrong formulas on dimensional grounds.

### Answer:According to dimensional analysis an equation must be dimensionally homogeneous.  ## Question 2. 15. A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ m0 of a particle in terms of its speed v and the speed of light c. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes: ## Guess where to put the missing c. ## Question 2.22. Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity): (a) the total mass of rain-bearing clouds over India during the Monsoon (b) the mass of an elephant (c) the wind speed during a storm (d) the number of strands of hair on your head (e) the number of air molecules in your classroom.

### Answer:(a) The average rainfall of nearly 100 cm or 1 m is recorded by meteorologists, during Monsoon, in India. If A is the area of the country, then A = 3.3 million sq. km = 3.3 x 106(km)2 = 3.3 x 106x 106m2= 3.3 x 1012m2 Mass of rain-bearing clouds = area x height x density = 3.3 x 1012x 1 x 1000 kg = 3.3 x 1015kg. (b) Measure the depth of an empty boat in water. Let it be d1. If A be the base area of the boat, then volume of water displaced by boat, V1 = Ad2 Let d2 be the depth of boat in water when the elephant is moved into the boat. Volume of water displaced by (boat + elephant), V2 = Ad2 Volume of water displaced by elephant, V = V2-V1 = A(d2 -d1) If p be the density of water, then mass of elephant = mass of water displaced by it = A(d2 – d1) p. (c) Wind speed can be estimated by floating a gas-filled balloon in air at a known height h. When there is no wind, the balloon is at A. Suppose the wind starts blowing to the right such that the balloon drifts to position B in 1 second. Now, AB = d = hθ. ## Question 2. 28. The unit of length convenient on the nuclear scale is afermi: I f=10-15m. Nuclear sizes obey roughly the following empirical relation: r = r0 A1/3 where r is the radius of the nucleus, A its mass number, and r0 is a constant equal to about,1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise 2.27.

### Answer:Assume that the nucleus is spherical. Volume of nucleus = 4/3 πr3= 4/3 π [r0A1/3]3= 4/3 πr03A Mass of nucleus = A .•. Nuclear mass density = Mass of nucleus/Volume of nucleus = A/(4/3πr03A) = 3/4πr03 Since r0 is a constant therefore the right hand side is a constant. So, the nuclear mass density is independent of mass number. Thus, nuclear mass density is constant for different nuclei. For sodium, A = 23 .’. radius of sodium nucleus, r = 1.2 x 10-15(23)1/3m = 1.2 x 2.844 x 10-15m =3.4128 x 10-15 ## Question 2. 29. A LASER is source of very intense, monochromatic, and unidirectional beam of light. These properties of a laser light can be exploited to measure long distances. The distance of the Moon from the Earth has been already determined very precisely using a laser as a source of light. A laser light beamed at the Moon takes 2.56 s to return after reflection at the Moon’s surface. How much is the radius of the lunar orbit around the Earth?

### Answer:We known that speed of laser light = c = 3 x 108m/s. If d be the distance of Moon from the earth, the time taken by laser signal to return after reflection at the Moon’s surface ## Question 2. 33. A great physicist of this century (P.A.M. Dirac) loved playing with numerical values of fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (c, e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (-15 billion years). From the table of fundamental constants in this book, try to see if you too can construct this number (or any other interesting number you can think of). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants?

### Answer:The values of different fundamental constants are given below: ### We have to try to make permutations and combinations of the universal constants and see if there can be any such combination whose dimensions come out to be the dimensions of time. One such combination is: 