Tạp chí Physics For You - tháng 12/2017

Volume 25 Managing Editor Mahabir Singh Editor Anil Ahlawat No. 12 December 2017 Corporate Office: Plot 99, Sector 44 Institutional area, Gurgaon -122 003 (HR). Tel : 0124-6601200 e-mail : [email protected] website : www.mtg.in Regd. Office: 406, Taj Apartment, Near Safdarjung Hospital, New Delhi - 110029. CONTENTS Class 11 NEET | JEE Essentials 8 Exam Prep 23 Ace Your Way CBSE : Series 6 29 MPP-8 38 Brain Map 42 Class 12 Brain Map 43 NEET | JEE Essentials 44 Exam Prep 60 Ace Your Way CBSE : Series 7 67 MPP-8 75 Competition Edge Olympiad Problems 79 Physics Musing Problem Set 53 82 JEE Work Outs 84 Physics Musing Solution Set 52 88 Subscribe online at www.mtg.in Individual Subscription Rates Combined Subscription Rates 1 yr. 2 yrs. 3 yrs. 1 yr. 2 yrs. 3 yrs. Mathematics Today 330 600 775 PCM 900 1500 1900 Chemistry Today 330 600 775 PCB 900 1500 1900 Physics For You 330 600 775 PCMB 1000 1800 2300 Biology Today 330 600 775 Send D.D/M.O in favour of MTG Learning Media (P) Ltd. 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PHYSICS FOR YOU | DECEMBER ‘17 7 Unit 6 PROPERTIES OF BULK MATTER i.e., Stress v Strain Stress = K Strain =5381>93C?6C?<94C Elasticity The property of the material to recover its original shape or size on the removal of deforming force is known as elasticity. x If a body completely regains its original form after removal of external force, it is called a perfectly elastic body. x If the body remains deformed and shows no tendency to recover its original condition on removal of external forces, is said to be perfectly plastic. x Strain : The ratio of change in length, volume or shape of body to its original configuration is called strain. Strain may be longitudinal, volume or shearing. As it is the ratio of two similar quantities, it is a pure number and has no unit. x Stress : The restoring force developed per unit area in the body when subjected to deforming force is Restoring force = F/A called stress, i.e., Stress = area –2 SI unit is N m The dimensional formula for stress is [ML–1 T –2]. Hooke’s Law and Stress-Strain Curve x Hooke’s Law : For small deformations the stress developed in the body is directly proportional to the strain of the body. 8 PHYSICS FOR YOU | DECEMBER ‘17 K= x Stress where, K = modulus of elasticity Strain Modulus of Elasticity (K) : The ratio of stress developed to the strain produced in the body is called modulus of elasticity. Stress K= Strain Its SI unit is N m–2 and dimension is [ML–1T –2] Stress-strain curve The given graph is a tensile simple case of metallic wire which is subjected to increasing tension. O ¾ From O to A, the curve is linear and body can regain its original shape after removing stress i.e., Hooke’s Law is obeyed. ¾ From A to B, stress is not proportional to strain but the body still can regain its original shape. ¾ Point B, is the yield point (or elastic limit) on further increasing stress beyond the point B, the body will have a permanent set after removing the stress. PHYSICS FOR YOU | DECEMBER ‘17 9 ¾ ¾ From B to C and further upto D strain changes rapidly for smaller stress. E is the fracture point where the body breaks on applying further strain. Elastic Potential Energy 1 x Energy density = × stress × strain 2 1 = × Y × (strain)2. 2 1 x Workdone = × stress × strain × volume 2 (stress)2 x Workdone per unit volume = . 2Y x For elastic constants : inter relations Y = Young’s modulus, K = Rigidity modulus B = Bulk modulus, V = Poisson’s ratio ¾ Y = 2K(1 + V) ¾ Y = 3B(1 – 2V) 9B η 9 3 1 . = + or Y = ¾ η + 3B Y η B 3B − 2η σ= ¾ 6B + 2η x Applications ¾ Designing a beam for construction of roofs l and bridges. b = breadth of slab Y = Young’s modulus of slab d = thickness of slab l = length Wl 3 The depression in rectangular beam, δ = 4Y bd 3 or G v(l)3 ?To minimize the depression in the beam or slab short length slabs are used. For a beam with circular cross-section of radius r depression is, δ = ¾ 12πr 4Y A hollow shaft is stronger than a solid shaft of same mass, length and material. Torque required to produce a unit twist in solid πηr 4 shaft (bar) τ solid = 2L and torque for hollow shaft, τ hollow = 10 Wl 3 ( πη r2 4 − r14 2L ) PHYSICS FOR YOU | DECEMBER ‘17 ∴ or τ solid r4 = 4 τ hollow r − r 4 2 1 ( )( r22 + r12 r22 − r12 τ hollow r2 4 − r14 = = τ solid r4 r4 τ hollow r22 + r12 ≅ >1 τ solid r2 {' ( ) r 2 ≅ r22 − r12 )} Illustration 1 : A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then what is the elastic energy stored in the wire ? Soln.: Elastic potential energy 1 1 F ΔL = × stress × strain × volume = × × × (AL) 2 2 A L 1 1 = F ΔL = × 200 × 10 −3 = 0.1 J 2 2 8I4B?CD1D93C*6<E94C1DB5CD Pressure Due to Liquid x The thrust exerted by a liquid at rest per unit area of the substance in contact with the liquid is called pressure. If F is the thrust exerted by a liquid on a surface of small area 'A, then pressure is given by P = lim (F / ΔA) ΔA→0 x x x x x x The unit of pressure is dyne cm–2 in CGS system and N m–2 in SI. A pressure of one N m–2 is also called pascal. Pascal’s law : Pressure applied to enclosed liquid is transmitted equally in all directions, to every position of liquid and wall of container. Hydrostatic pressure of liquid column : Pressure = Ugh where U = density of liquid, h = height of liquid column. Brahma’s hydraulic press is based upon Pascal’s law of liquid pressure. Unit of pressure is pascal. Its symbol is Pa. Bar = 105 Pa, torr = 1 mm of Hg column. Density and relative density : Density = mass/volume. For water, density = 103 kg m–3. 3 –2 3 ¾ One litre = 1000 cc = 1000 cm = 1000 × (10 m) –3 3 = 10 m . Density of substance ¾ Relative density = Density of water at 4 °C