RAVI AGARWAL (M.SC.)- 9913650950 / 9374727052

TIME: 3 Hrs. CH. Full Course MARKS: 80

Q.I Questions numbers 1 to 30 are objectives, carrying ONE mark each. (30) 1. 1microgram (μg) = _____ 1 kilogram (Kg.).

(a) 106 (b) 10-5 (c) 10-6 (d) 108

2 A rubber eraser 3cm×1cm×8cm is clamped at one end with the 8 cm edge vertical. A horizontal force of 2.4 N is applied at the free end (the top face). If the shear modulus of rubber is 1.6×105 Nm-2, the horizontal displacement of the top face will be ______. (a) 1mm (b) 2mm (c) 3mm (d) 4mm3 Two wires A and B have equal lengths and are made of the same material, but the diameter of wire A is twice that of wire B. Then, for a given load. (a) the extension of B will be four times that of A. (b) the extension of A and B will be equal (c) the strain in B is four times that in A. (d) Both (a) & (C) 4 The ratio of number density of same gas molecules in two different containers is 1:9. What is the ratio of their mean free path? 5 What is elastic hysteresis? 6 What is triple point?7 What does εv & εs represents? 8 What do you mean by angular variables? 9 What is Thermal Steady state? 10 What is Shearing stress? 11 Write the value and unit of Boltzmann constant. 12 State: Stefan-Boltzmann’s law. 13 State the arguments given by Ptolemy and Copernicus 14 On what factors the efficiency of Carnot cycle depends? 15 What is SHM? 16 1 amu = ______ mg. 17 What is the linear dimension of an atom? 18 What is dimensional analysis? 19 What is the origin of friction? 20 What is inertia? 21 Why it is necessary to mention reference point for Torque and angular momentum? 22 What is latitude? 23 Give two situations of zero acceleration. 23 What is Heat Capacity? 24 What happen to coefficient of friction, when weight of body is doubled? 25 State the law of conservation of momentum. 26 When resultant force is zero then velocity of its c.m. is either _____ OR ______. 27 What is meant by moment of couple? 28 Out of all the solids, liquids and gases which will possess all the moduli of elasticity? 29 Write equations of natural angular frequency and natural frequency of a simple pendulum of length l. 30 What is Solar constant?

Q.III Question number 31 to 40 are short answer questions, each carries TWO marks (20) 31 Explain how dimensional analysis can be used to derive equation for a physical quantity in terms of other physical quantities. 32 Give physical explanation of the definition of torque. 33 Deduce Kepler’s second law of planetary motion.34 What should be the period of rotation of earth about its own axis, so that the effective acceleration due to gravity becomes zero at the equator?35 In how many categories the crystalline solid substances are classified? Discuss molecular solid and ionic solid. 36

Accept F1 = mV x

2

l an force experienced by the wall due to collision of 1 molecule and derive

expression for pressure of ideal gas. P = 13

𝛒 < V 2 >

37 Derive M.I. of a thin uniform rod about on axis passing through its centre of mass and perpendicular to its length.

38 Obtain the expression: d p⃗dx

¿ F⃗

39 Explain: Average velocity and Average speed.40 Define periodic time for SHO and hence obtain equation for periodic time for spring mass system and explain.

Q.IV Question number 41 to 50 are short answer question each carries THREE marks (30) 41 Two boats, A and B, move away from buoy anchored at the middle of a river along the mutually perpendicular straight lines: the boat A along the river, and the boat B across the river. Having moved off an equal distance from the buoy the boats returned. Find the ratio of times of motion of boats τA / τB if the velocity of each boat w.r.t. water is 1.2 times greater than the stream velocity. 42 A steel wire is hanged vertically. What should be its maximum length so that it does not break by its own weight? The density of steel is 7.8 g/cm3 and the breaking stress for steel is 7.8 ×109dyne/cm2. 43 Two blocks, each of mass 3kg, are connected by a light string and placed on a horizontal surface. If a force of 20 N is applied in the horizontal direction on either of these blocks, the acceleration of each block is 0.5 ms-2. Assuming that the frictional forces on the two blocks are equal, calculate the tension produced in the string. 44 What is gravitational potential? Find the gravitational potential near the surface of earth? 45 An extremely thin disc of radius R, having surface (mass) densityρ. A small disc of radius R/2 is cut from it. Find the C.M. of the remaining part of the disc w.r.t. the C.M. of the original disc. 46 The mass and radius of hollow cylinder are 2 kg and 0.2 m respectively. The cylinder can be rotated about its geometrical axis. A thin string is wound on the cylinder. Now, a force of 50 N is applied at the free end of the string such that the force acts tangentially to the surface of the cylinder. As a result of this the cylinder starts rotating. Find the following : (1) Torque on the cylinder (2) Angular acceleration of the cylinder (3) Angular velocity after 2 sec (4) Angular momentum after 2 sec (5) Rotational kinetic energy after 2 sec (6) Angular displacement after 2 sec. (7) Work done during 2 sec (8) Power after 2 sec.

47 A rigid body rolls from the top of in dined plane using the formula v2 =

2 gh

1+ k2

R2

, derive the

expression for the decrease in acceleration due to frictional force acting on rolling body. 48 Breaking stress of rope having area of cross-section A is σ. By using this rope a mass m is being lifted upward. Then what maximum acceleration can be produced in it? 49 A spring of length l and force- constant k is cut into two parts of length l1 and l2. Here l1 = nl2. Obtain force constant k1 and k2 respectively of these parts in terms of n and K 50 The equation of a progressive, harmonic waves travelling in a medium is given by an equation yi = Acos(ax+bt); where A, a and b are positive constants. This wave is reflected from the rigid support kept at x = 0. The intensity of the reflected wave is 0.64 times that of the incident wave. (a) What are wavelength and frequency of the incident wave? (b) Write the equation of the reflected wave. (c) Express the resultant wave, obtained due to superposition of the incident and reflected waves, in the form of the progressive and stationary waves.

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