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KENDRIYA VIDYALAYA NO. :- 1, BHOPAL Half Yearly Examination November- 2016 Class XI (Physics)-answers Time : 3 Hrs. M.M. 70 SECTION 'A' Ans :-1 A related effort is to derive the properties of a bigger, more complex, system from the properties and interactions of its constituent simpler parts. This approach is called reductionism and is at the heart of physics. For example, the subject of thermodynamics, developed in the nineteenth century, deals with bulk systems in terms of macroscopic quantities such as temperature, internal energy, entropy, etc. Subsequently, the subjects of kinetic theory and statistical mechanics interpreted these quantities in terms of the properties of the molecular constituents of the bulk system. In particular, the temperature was seen to be related to the average kinetic energy of molecules of the system. Ans:- 2 A large force acting for a short time to produce a finite change in momentum is called an impulsive force. Ans:-3 Ans:- 4 If the external torque is zero, Ans:- 5 The ratio of hydraulic stress to the corresponding hydraulic strain is called bulk modulus. It is denoted by symbol B. Ans:-6 Ans:-7 Large distances such as the distance of a planet or a star from the earth cannot be measured directly with a metre scale. An important method in such cases is the parallax method. To measure the distance D of a far away planet S by the parallax method, we observe it from two different positions (observatories) A and B on the Earth, separated by distance AB = b at the same time as shown in Fig. below. We measure the angle between the two directions along which the planet is viewed at these two points. The ASB in Fig. represented by symbol θis called the parallax angle or parallactic angle.As the planet is very far away, therefore, θ is very small. Then we approximately take AB as an arc of length b of a circle with centre at S and the distance D as and Ans:- 8 Ans:- 9 OR Ans:- 10 The change in kinetic energy of a particle is equal to the work done on it by the net force. i.e. Change in K. E. = Work done. Section- C 11. Gravitational Force:The gravitational force is the force of mutual attraction between any two objects by virtue of their masses. It is a universal force. Every object experiences this force due to every other object in the universe. All objects on the earth, for example, experience the force of gravity due to the earth. In particular, gravity governs the motion of the moon and artificial satellites around the earth, motion of the earth and planets around the sun, and, of course, the motion of bodies falling to the earth. Electromagnetic Force:Electromagnetic force is the force between charged particles. In the simpler case when charges are at rest, the force is given by Coulomb’s law : attractive for unlike charges and repulsive for like charges. Charges in motion produce magnetic effects and a magnetic field gives rise to a force on a moving charge. Electric and magnetic effects are, in general, inseparable – hence the name electromagnetic force. Like the gravitational force, electromagnetic force acts over large distances and does not need any intervening medium. It is enormously strong compared to gravity. Strong Nuclear Force:The strong nuclear force binds protons and neutrons in a nucleus. It is evident that without some attractive force, a nucleus will be unstable due to the electric repulsion between its protons. This attractive force cannot be gravitational since force of gravity is negligible compared to the electric force. A new basic force must, Therefore, be invoked. The strong nuclear force is the strongest of all fundamental forces, about 100 times the electromagnetic force in strength. It is charge-independent and acts equally between a proton and a proton, a neutron and a neutron, and a proton and a neutron. Its range is, however, extremely small, of about nuclear dimensions (10–15 m). It is responsible for the stability of nuclei. The electron, it must be noted, does not experience this force. Weak Nuclear Force:- OR NAME OF SCIENTIST MAJOR CONTRIBUTION J.C. Bose C.V. Raman Ultra short radio waves Inelastic scattering of light by molecules M.N. Saha Thermal ionisation S.N. Bose Quantum statistics Homi Jehangir Bhabha Cascade process of cosmic radiation S. Chandrasekhar Chandrasekhar limit, structure and evolution of stars Q:-12 Absolute Error:- The magnitude of the difference between the individual measurement and the true value of the quantity is called the absolute error of the measurement. This Relative Error:- The relative error is the ratio of the mean absolute error amean the quantity measured. Percentage Error:When the relative error is expressed in per cent, it is called the percentage error Q:-13 . to the mean value amean of For uniformly accelerated motion, we can derive some simple equations that relate displacement (x), time taken (t), initial velocity (v), final velocity (v0) and acceleration (a). Acceleration a = time rate of change of velocity of a body a = (v-v0 )/ t v = v0 + at the displacement x of the object is Q:-14 Consider two objects A and B moving uniformly with average velocities VA and VB in one dimension, say along x-axis. If xA (0) and xB (0) are positions of objects A and B, respectively at time t = 0, their positions XA (t) and xB (t) at time t are given by: the velocity of object B relative to object A is Relative velocity of ground with respect to Q:-15 Q:-16 Centripetal Acceleration:- The acceleration of an object moving with speed v in a circle v /R and is always directed towards the centre is of radius R has a magnitude 2 called centripetal acceleration. Therefore centripetal acceleration Q:-17 The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts. The unit of force has not been defined so far. We, therefore, have the liberty to choose any constant value for k. For simplicity, we choose k = 1. The second law then is The retardation ‘a’ of the bullet (assumed constant) is given by The retarding force, by the second law of motion, is Q:-18 Banking of a road:- To reduce the contribution of friction to the circular motion of the vehicle outer edge of the road is raised at some angle than inner edge this is called banking of road. There is no acceleration along the vertical direction, the net force along this direction must be zero. Hence -1 The centripetal force is provided by the horizontal components of N and f. -2 From Equation 1 & 2, we get we see that maximum possible speed of a car on a banked road is greater than that on a flat road. Q:-19 Q:-20 A collision in which momentum and kinetic energy remains conserved is known as elastic collision. A collision in which only momentum remains conserved is called in-elastic collision. A collision in which the two particles move together after the collision is called a completely inelastic collision. The intermediate case where the deformation is partly relieved and some of the initial kinetic energy is lost is more common and is appropriately called an inelastic collision. Consider first a completely inelastic collision in one dimension. Then, in Fig. From above two equations we get, Also except answer if student derive for particular two bodies. Q:-21 Escape Velocity:The minimum speed required for an object to escape from the surface of earth or from influence of earth gravitational force is called escape velocity. Suppose the object did reach infinity and that its speed there was V. The energy of an object is the sum of potential and kinetic energy. The total energy of the projectile at infinity then is ---------1 ---------2 From equation (1) & (2); applying principle of conservation of energy; -------------3 The minimum value of Vi corresponds to the case when the L.H.S. of Eq. (3) equals zero. Q:-22 Variation in “g” with height:- Variation in “g” with depth:- Section –D Q:- 23 (b) (i) 800 N (ii) 400 N (iii) 1200 N Section –E 24-a) we know Distance covered by body in “t” seconds :S (t) = ut + ½ at2 Distance covered by body in “(t-1)” seconds :- S(t-1) = u(t-1) + ½ a (t-1)2 Distance covered by body in “(tth)” seconds :- S(t) - S(t-1) = u + ½ a(2t-1) 24-b h = ut + ½ gt2 Distance covered in first “3” seconds = 3u + ½ g (3)2 Distance covered in “last second of motion” seconds = u + ½ g (2t-1) According to question; 3u + 1/2g (9) = u + ½ g(2t-1) 2u = ½ g(2t-10) u = ½ g ( t-5) Since ball is dropped u =0 ; therefore 0 = t-5 We get; t=5 sec. H = ½ ×10×25 = 125 m OR a- Time of flight:Time taken by the projectile to reach the maximum height :- Since at this point Therefore; Horizontal Range :The horizontal distance travelled by a projectile from its initial position (x = y = 0) to the position where it passes y = 0 during its fall is called the horizontal range, R. It is the distance travelled during the time of flight T . Therefore, the range R is b- Your by putting any two values to show the same may be excepted Q:-25 a) Theorem of perpendicular axes the moment of inertia of a planar body (lamina) about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with perpendicular axis and lying in the plane of the body. Theorem of parallel axes The moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass and the square of the distance between the two parallel axes. b OR A) . B) . Q;-26 a) Stress:- The internal restoring force acting per unit area of a deformed body is called stress i.e. S = External deforming force/ area S.I. Unit of Nm-2 Types of Stress:- 1) Normal Stress :- When a deforming force acts normally over an area of a body, then the internal restoring force set up per unit area of the body is called the normal stress. Normal stress can be sub divided into following categories:a) Tensile stress b) Compressive stress c) Hydraulic stress 2) Tangential or Shearing Stress :- When a deforming force, acting tangentially to the surface of a body produces a change in the shape of the body without any change in volume, then the stress set up in the body is called tangential stress. a) Strain :- The ratio of change in configuration to the original configuration is called strain. i.e. Strain = Change in configuration/ Original Configuration Types of Strain:1) Longitudinal Strain:- If the deforming force prodces a change in length alone, the strain produced in the body is called Longitudinal strain or tensile strain. 2) Volumetric Strain:- If the deforming force produces a change in volume alone, the strain produced in the body is called volumetric strain. 3) Shearing Strain:- If the deforming force produces a change in the shape of the body wihout changing its volume, the strain produced is called shearing strain. The point B in the curve is known as yield point (also known as elastic limit) and the corresponding stress is known as yield strength of the materi The point D on the graph is the ultimate tensile strength ) of the material. Beyond this point, additional strain is produced even by a reduced applied force and fracture occurs at point E. If the ultimate strength and fracture points D and E are close, the material is said to be brittle. If they are far apart, the material is said to be ductile. In case, even when the stress is zero, the strain is not zero. The material is said to have a permanent set. The deformation is said to be plastic deformation. Or a) Young Modulus of Elasticity:- It is defined as the ratio of normal stress to the longitudinal strain with in the elastic limit. FL Y= r 2 l S.I. unit of Young’s Modulus is N/m2 Steel is more elastic than rubber, because value of “Y” of steel is more than rubber. b)