Electronic devices except non-programmable calculators are not allowed in the Examination Hall.<\/li>\n<\/ul>\nQuestion 1.
\nPick the odd one out among the following forces:
\na. Gravitational force
\nb. Weak nuclear force
\nc. Viscous force
\nd. Electromagnetic force<\/p>\n
Question 2.
\nThe demonstration of conservation of angular momentum is schematically shown in the figures.
\n
\nIdentify the figure which has more angular velocity.<\/p>\n
Question 3.
\n\u201cTwo systems in thermal equilibrium with a third system, are in thermal equilibrium with each other\u201d. Identify the law given by the above statement.<\/p>\n
Question 4.
\nA steel rod has a radius of 10 mm and a length of 1.0 m. A 100 kN force stretches it along its length. Calculate the elongation of the steel rod. [Young\u2019s modulus of steel is 2.0 \u00d7 1011<\/sup> N\/m2<\/sup>.]
\nOR
\nA metal cube of side 10 cm is subjected to a; shear stress 104<\/sup> N\/m2<\/sup>. Calculate the rigidity: modulus, if the top of the cube is displaced by 0.05 cm with respect to its bottom.<\/p>\nQuestion 5.
\nDraw the schematic diagram of a hydraulic lift. Give its working principle.<\/p>\n
Question 6.
\nEstimate the average thermal energy of the helium atom at a temperature of 27\u00b0C. [Boltzmann constant is 1.38 \u00d7 10-23<\/sup>J\/K.]<\/p>\nQuestion 7.
\nThe graph below exhibits the anomalous expansion of water.
\n
\nBased on the graph, explain how lakes freeze from the top to bottom rather than from bottom to top.<\/p>\n
Question 8.
\nMatch the following in three columns.
\n<\/p>\n
Question 9.
\na. The figure below shows the \u2018parallax method\u2019 to measure the distance \u2018D\u2019 of a planet \u2018S\u2019 from the earth.
\n
\nMark the parallax angle \u20180\u2019 in the figure. Explain how the distance \u2018D\u2019 can be measured.
\nb. Check whether the equation mv2<\/sup> = mgh is dimensionally consistent. Based on the above equation, justify the following statement. \u201cA dimensionally correct equation need not be actually an exact equation\u201d.<\/p>\nQuestion 10.
\na. Choose the correct statement\/statements related to uniform circular motion.
\ni. The acceleration in uniform circular motion is tangential to the circle.
\nii. The acceleration in uniform circular motion is directed radially inwards.
\niii. The velocity in uniform circular motion has constant magnitude.
\niv. The velocity in uniform circular motion is directed radially inwards.
\nb. A particle is projected up into the air from the point with a speed of 20 m\/s at an angle of projection 30\u00b0. What is the maximum height reached by it?<\/p>\n
Question 11.
\na. The escape speed from the surface of the earth is given by …………………..
\n
\nb. An artificial satellite circulating the earth is at a height 3400 km from the surface of the earth. If the radius of the earth is 6400 km and g = 9.8 m\/s2<\/sup>, calculate the orbital velocity of the satellite.<\/p>\nQuestion 12.
\na. Among the following, which are examples of simple harmonic motion?
\ni. The rotation of the earth about its axis.
\nii. Vertical oscillations of a loaded spring.
\niii. Oscillations of a simple pendulum.
\niv. Uniform circular motion.
\nb. The displacement in simple harmonic motion can be represented as x(t) = A Cos(\u03c9t+ \u03a6), where \u2018\u03a6\u2019is the phase constant. Identify and define \u2018A\u2019 and \u2018co\u2019 in the equation.<\/p>\n
Question 13.
\na. A transverse harmonic wave is described j by y=3.0 Sin (0.018 \u00d7 + 36t), where \u2018x\u2019 and \u2018y\u2019 are in cm. The amplitude of this; wave is _________
\nb. The figure below shows the fundamental mode or first harmonic in a stretched j string when a standing wave is formed ‘ in the string.
\n
\nDraw the figure that shows the second; harmonic in the string. If \u2018L\u2019 is the length of the string and Vis the speed of the: wave in the string, what are the equations of first and second harmonic frequent:<\/p>\n
Question 14.
\nAn object released near the surface of the I earth is said to be in free fall. (Neglect the air resistance)
\na. Choose the correct alternative from the clues given at the end of the statement. \u201cFreefall is an example of accelerated motion\u201d.
\nb. The incomplete table shows the velocity (\u03c5) of a freely falling object in a time interval of 1 s. (Take g = 10 m\/s2<\/sup>)
\n
\nComplete the table and draw the velocity-time graph.
\nc. Area under velocity-time graph gives.<\/p>\nQuestion 15.
\nThe schematic diagram of the circular motion of a car on a banked road is shown in the figure.
\n
\na. If the centripetal force is provided by the horizontal components of \u2018N\u2019 and \u2018F\u2019 arrive at an expression for maximum safe speed.
\nb. The optimum speed of a car on a banked road to avoid wear and tear on its tyres is given by …………….
\n<\/p>\n
Question 16.
\nEnergy of a body is defined as its capacity of doing work\u201d.
\na. The energy possessed by a body by virtue of motion is known as ………….
\nb. A body of mass 5 kg initially at rest is subjected to a horizontal force of 20 N. What is the kinetic energy acquired by the body at the end of 10 s?
\nc. State whether the following statement is TRUE or FALSE. \u201cThe change in kinetic energy of a particle is equal to the work done on it by the net force\u201d.<\/p>\n
Question 17.
\nThe angular momentum of a particle is the rotational analogue of its linear momentum.
\na. The equation connecting angular momentum and linear momentum are ……………
\n
\nb. Starting from the equation connecting angular momentum and linear momentum, deduce the relation between torque and angular momentum.
\nOR
\nThe moment of inertia in rotational motion is analogous to mass in linear motion.
\na. The moment of inertia of a circular disc about an axis perpendicular to the plane, at the center is given by ………….
\n
\nb. State perpendicular axis theorem and by using the theorem, deduce the moment of inertia of the circular disc about an axis passing through the diameter.<\/p>\n
Question 18.
\nA region of streamlined flow of an incompressible fluid is shown in the figure.
\n
\na. By considering mass conservation in the fluid flow, arrive at the \u2018equation of continuity\u2019.
\nb. The onset of turbulence in a fluid is determined by ‘Reynolds number’, given as …………….
\n<\/p>\n
OR<\/p>\n
Schematic diagram of capillary rise in a narrow tube is shown in the figure.
\n
\na. Arrive at an expression for capillary height ‘h’ in terms of the surface tension of the liquid.
\nb. On the surface of the moon, the liquid in a capillary tube will rise to the ……………..
\ni. same height as on earth
\nii. less height as on earth
\niii. more height than that on earth
\niv. infinite height.<\/p>\n