I. Answer the following questions: ( 10 \u00d7 1 = 10)<\/span><\/p>\nQuestion 1.
\nName the experiment which established the nuclear model of atom.
\nAnswer:
\nGeiger-Marsdon experiment on alpha-particle scattering by gold foil.<\/p>\n
Question 2.
\nWhat is S.I. unit of luminous intensity?
\nAnswer:
\nThe SI unit luminous intensity is candela (cd).<\/p>\n
Question 3.
\nGive an example for two dimensional motion.
\nAnswer:
\nProjectile motion and circular motion.<\/p>\n
Question 4.
\nWhy don\u2019t action and reaction forces cancel each other?
\nAnswer:
\nAction and reaction forces act on two interacting bodies, so the forces don\u2019t cancel each other.<\/p>\n
<\/p>\n
Question 5.
\nA light body and a heavy body have the same momentum. Which one will have greater kinetic energy?
\nAnswer:
\nSince K.E. \u221d \\(\\frac{1}{m}\\) for same linear momentum, lighter body has more kinetic energy.<\/p>\n
Question 6.
\nGive the expression for moment of inertia of a circular disc of radius R about its diameter.
\nAnswer:
\nI = \\(\\frac{M R^{2}}{4}\\)<\/p>\n
Question 7.
\nWhat are geostationary satellites?
\nAnswer:
\nGeo-stationary satellites orbit around the Earth with the speed of the satellite equal to the rotational speed of the Earth. Hence, these satellites appear to be fixed with respect to a place on the surface of the Earth.<\/p>\n
Question 8.
\nWhat is shear deformation?
\nAnswer:
\nShear deformation is the ratio of lateral displacement of one edge to the vertical distance between the opposite faces of the body.<\/p>\n
Question 9.
\nHow does melting point of ice changes with increase of pressure?
\nAnswer:
\nThe ice will go to a lower melting point.<\/p>\n
<\/p>\n
Question 10.
\nGive an example for a wave which can travel through vacuum.
\nAnswer:
\nElectromagnetic wave.<\/p>\n
Part – B<\/span><\/p>\nII. Answer any FIVE of the following questions: ( 5 \u00d7 2 = 10 )<\/span><\/p>\nQuestion 11.
\nGiven the relative error in the measurement of the radius of a circle is 0.02, whal is the percentage error in the measurement of its area?
\nAnswer:
\nA = \u03c0r2<\/sup>
\n\\(\\frac{\\Delta \\mathrm{A}}{\\mathrm{A}}=2 \\mathrm{r} \\frac{\\Delta r}{r}\\)
\n= 2 \u00d7 r \u00d7 0.02 = 0.04r
\n(\\(\\frac{\\Delta \\mathrm{A}}{\\mathrm{A}}\\)) = 0.04r<\/p>\nQuestion 12.
\nWhat are the significance of velocity – time graph?
\nAnswer:
\nThe slope of the line on a v-t graph gives the acceleration of the particle.<\/p>\n
Question 13.
\nWhat is resolution of a vector? What is the x-component of a vector A, that makes an angle 300 with x-axis.
\nAnswer:
\nA single vector can be resolved in two or more number of directions each of which is known as the component of a vector. This splitting is known as resolution of vector.
\n\\(\\overrightarrow{\\mathrm{A}}_{x}=\\left(A \\cos 30^{\\circ} \\hat{i}\\right)=\\frac{\\sqrt{3}}{2} \\hat{i}\\)<\/p>\n
<\/p>\n
Question 14.
\nGive the general conditions of equilibrium of a rigid body.
\nAnswer:
\n(1) The vector sum of the forces on the rigid body is zero for translatory equilibrium
\n\\(\\sum_{i=1}^{n} \\vec{F}_{i}=0\\) and (acceleration a = 0 )
\n(2) The vector sum of the torques on the rigid body is zero for rotatory equilibrium (a=0) i.e.
\n
\ni.e., the components of X, Y, and Z independently vanish to zero for linear equilibrium.
\n
\nSum of X components, Y components and Z components of torque on the particles, vanish for rotational equilibrium.<\/p>\n
Question 15.
\nWrite Stoke\u2019s formula for viscous drag force. Explain the terms.
\nAnswer:
\nF = 6\u03c0\u03b7av where v – terminal speed of liquid, \u03b7 – coefficient of viscosity, a – radius of the spherical object and F – viscous drag force.<\/p>\n
Question 16.
\nWhat is meant by anomalous behavior of water. What is its significance?
\nAnswer:
\nThe density of water increases from 0\u00b0C to 4\u00b0C and thereafter decreases with increase of temperature.
\n
\nThis behaviour of water from 0\u00b0C to 4\u00b0C is known as anomalous expansion of water. Water at 4\u00b0C has the maximum density and sinks down. However, water below the surface, relatively having lower density, rises above. Water becomes lighter as the temperature falls below 4\u00b0C. Ice at 0\u00b0C has the minimum density and floats on water. Hence marine animals can survive below ice. It is water everywhere below ice.<\/p>\n
<\/p>\n
Question 17.
\nState and explain first law of thermodynamics.
\nAnswer:
\nThe energy (\u2206Q) supplied to the system goes in partly to increase the internal energy of the system (\u2206U) and the rest in doing work on the environment (\u2206W).
\n\u2206Q = \u2206U + \u2206W
\nwhere \u2206Q \u2192 heat supplied, \u2206U \u2192 change in internal energy, \u2206W \u2192 work done<\/p>\n
Question 18.
\nWhat is periodic motion. Give an example.
\nAnswer:
\nA particle event that repeats itself in regular intervals of time is known as the periodic motion. Both circular and elliptical motions of electrons around the atomic nucleus are examples of periodic motions.<\/p>\n
Part – C<\/span><\/p>\nIII. Answer any FIVE of the following questions : ( 5 \u00d7 3 = 15 )<\/span><\/p>\nQuestion 19.
\nDerive the expression for time of flight of a projectile.
\nAnswer:
\nExpression for time of flight:
\n
\nConsider v = (v0<\/sub> sin\u03b8) – gt
\nPut v = 0, fort = time of ascent = ta
\n<\/sub>ta<\/sub> = \\(\\frac{v_{0} \\sin \\theta}{g}\\)
\nbut time of ascent = time of descent
\nand time of flight T = ta <\/sub>+ td<\/sub>
\ni.e., T = \\(\\frac{2 v_{0} \\sin \\theta}{g}\\) and T \u221d v0<\/sub> for a given angle of projection.<\/p>\n<\/p>\n
Question 20.
\nArrive at the statement of principle of conservation of linear momentum from Newton\u2019s laws of motion.
\nAnswer:
\nStatement: In an isolated system of collision of bodies, the total linear momentum before impact is equal to the total linear momentum after impact.
\n
\nLet m1<\/sub> and m2<\/sub> be the masses of two bodies moving along \\(\\vec{v}_{1 i}\\) and \\(\\vec{v}_{2 i}\\). Let \\(\\vec{v}_{1 f}\\) and be the \\(\\vec{v}_{2 f}\\) be final velocities after the impact.
\nAt the time of impact the force of action acts on the body B and the force of reaction acts on A.
\nApplying Newton\u2019s III law of motion
\n\\( |Force of action on \\mathrm{B}|=-| Force of reaction on \\mathrm{A} |\\)
\n
\nThis shows that the total final linear momentum of the isolated system equals its total initial momentum.<\/p>\nQuestion 21.
\nProve that potential energy stored in a spring is, where k is the force constant of the spring and x is the change in length Of the spring.
\nAnswer:
\nWork done by the spring force = Ws= \\(-\\int_{0}^{x_{\\mathrm{m}}} \\mathrm{F}_{\\mathrm{s}} \\mathrm{d} \\mathrm{x}\\)
\nW = \\(=-\\int_{0}^{x_{m}} \\mathrm{k} x \\mathrm{d} \\mathrm{x}\\)
\nW = \\(-\\frac{1}{2} \\mathrm{k} x_{\\mathrm{m}}^{2}\\)
\nWork done by the external pulling force = W= \\(\\frac{1}{2} \\mathrm{k} x_{\\mathrm{m}}^{2}\\)<\/p>\n
Question 22.
\nState Kepler\u2019s laws of planetary motion.
\nAnswer:
\nKepler\u2019s I law (Law of orbit): All planets revolve in elliptical orbits with Sun as one of its foci.
\n
\n2a – Major axis length
\n2b – Minor axis length
\nS-Sun at one focus P
\nS1<\/sup> – The other focus of the ellipse
\nP – Perihelion position of the planet.
\nA – Apehelion position of the planet.<\/p>\nKepler\u2019s II law (Law of areas) : The line joining the planet and the Sun sweeps out equal areas in equal intervals of time.
\n\\(\\frac{\\Delta \\overrightarrow{\\mathrm{A}}}{\\Delta \\mathrm{t}}=\\frac{1}{2 \\mathrm{m}} \\overrightarrow{\\mathrm{L}}\\)<\/p>\n
\nKepler\u2019s III law (Law of periods) : The square of the period of revolution of a planet around the sun is directly proportional to the cube of the semi major axis of the ellipse.
\ni.e., T2<\/sup> \u221d a3<\/sup> so that for two planets
\n\\(\\left(\\frac{T_{1}}{T_{2}}\\right)^{2}=\\left(\\frac{a_{1}}{a_{2}}\\right)^{3}\\)<\/p>\nQuestion 23.
\nProve that the centre of mass of a system moves with constant velocity in the absence of external force on the system.
\nAnswer:
\nWhen there is no external force the acceleration of the body is zero.
\nForce = rate of change of momentum.
\n
\n\u2234M is not zero
\nso this proves that velocity will always be constant in such scenario.<\/p>\n
Question 24.
\nState and explain Hooke\u2019s law. Define modulus of elasticity.
\nAnswer:
\nStatement: The ratio of stress to strain is a constant for a material within the elastic limit.
\nModulus of elasticity = \\(\\frac{\\text { Stress }}{\\text { Strain }}\\)<\/p>\n
Within the elastic limit, stress v\/s strain is a straight line \u2018A\u2019 is the elastic limit upto which Hooke\u2019s law is applicable. Beyond \u2018B\u2019 the yielding point, the wire extends but does not return to the initial state when the deforming force is removed. \u2018F\u2019 is the breaking point. \u2018EF\u2019 allows the material to be malleable and \u2018DE\u2019, ductile.
\n<\/p>\n
<\/p>\n
Question 25.
\nState Bernoulli\u2019s theorem. What are its applications?
\nAnswer:
\nAlong a steamline, in a steady flow of non viscous fluid, potential energy, kinetic energy and pressure energy remain constant.
\nApplications<\/p>\n