Way to Success Model Question Paper. Answer Key

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This method gives no information about the dimensionless constants in the formula like 1, 2,

1 A Way to Success Model Question Paper,aw;gpay; / PHYSICS Answer Key (Based on new Question pattern 2019) gphpt I / SECTION I 1 (c) 9 (b) 2 jpirntfk; velocity 10 (d) 3 AB cosθ; 11 (c) 4 v = f λ 12 (b) 5 (a) 13 (a) 6 (d) 14 (b) 7 (d) 15 (c) 8 (d) 16) gfjp II / Part II 17) 1. This method gives no information about the dimensionless constants in the formula like 1, 2,.π, e, etc. 2. This method cannot decide whether the given quantity is a vector or a scalar. Average velocity = Displacement = v Time interval avg = r t Velocity v = lim r = dr t 0 t dt wtsteam100@gmail.com

18) 19) The force acting on an object is equal to the rate of change of its momentum.

is not dissipated In Elastic Collision:- i) Total momentum is conserved ii) Total kinetic energy is not conserved iii) Forces involved are non -

20) 21) According to the principle of moments, a body will be in rotational equilibrium if algebraic sum of the moments of all forces acting on

It means for rotational equilibrium of a body sum of anticlockwise moments about a fixed point is equal to the sum of clockwise moments about the

2 18) 19) The force acting on an object is equal to the rate of change of its momentum. Elastic:- i) Total momentum is conserved ii) Total kinetic energy is conserved iii) Force involved are conservative forces iv) Mechanical energy is not dissipated In Elastic Collision:- i) Total momentum is conserved ii) Total kinetic energy is not conserved iii) Forces involved are non - conservative forces iv) Mechanical energy is dissipated in the heat, sound etc. 20) 21) According to the principle of moments, a body will be in rotational equilibrium if algebraic sum of the moments of all forces acting on the body, about a fixed point is zero. It means for rotational equilibrium of a body sum of anticlockwise moments about a fixed point is equal to the sum of clockwise moments about the same point. Newton's law of gravitation state that, a particle of mass M 1 attracts any other particle of mass M 2 in the universe with an attractive force. The strength of this force of attraction was found to be directly proportional to the product of their masses and is inversely proportional to the square of the distance between them. wtsteam100@gmail.com

22) 23) The ratio of lateral strain to longitudinal strain is called Poisson's ratio. μ = unit. No dimensions. lateral strain longitudinal strain.

kelvin or 1 0 C. Its SI unit is J Kg -1 K -1.

direction of propagation of waves. Example: Light (Electromagnetic waves) gfjp III / Part III 25) Rule Example 1.

All zeros to the right of a non - zero digit but to the left of a decimal point are significant. 4.

3 22) 23) The ratio of lateral strain to longitudinal strain is called Poisson's ratio. μ = unit. No dimensions. lateral strain longitudinal strain. No Specific heat capacity of a substance is defined as the amount of heat energy required to raise the temperature of 1 kg of a substance by 1 kelvin or 1 0 C. Its SI unit is J Kg -1 K ) In transverse wave motion, the constituents of the medium oscillate or vibrate about their mean positions in a direction perpendicular to the direction of propagation of waves. Example: Light (Electromagnetic waves) gfjp III / Part III 25) Rule Example 1. All non - zero digits are significant 2. all zeros between two non-zero digits are significant 3. All zeros to the right of a non - zero digit but to the left of a decimal point are significant. 4. a) the number without a decimal point, the terminal or trailing zero(s) are not significant has four significant figures 2008 has four significant figures Has five significant figures a) has three significant figures b) 30700m has five significant figures b) All zeros are significant if they come from a measurement. wtsteam100@gmail.com

26) The scalar product or dot product of two vectors is defined as the product of the magnitudes of both the vectors and the cosine of the angle between them.

B = AB cosθ Here, A and B are magnitudes of A and B 28) Objects on Earth experience the gravitational force of Earth. The gravitational force acting on an object of mass m is mg.

When we stand on the floor, there are two forces, acting downwards and the other is the normal force exerted by the floor upwards on us to keep us at rest.

4 26) The scalar product or dot product of two vectors is defined as the product of the magnitudes of both the vectors and the cosine of the angle between them. 27) Thus if there are two vectors A and B having an angle θ between them, then their scalar product is defined as A. B = AB cosθ Here, A and B are magnitudes of A and B 28) Objects on Earth experience the gravitational force of Earth. The gravitational force acting on an object of mass m is mg. This force always acts downwards towards the centre of the Earth. When we stand on the floor, there are two forces, acting downwards and the other is the normal force exerted by the floor upwards on us to keep us at rest. The weight of an object W is defined as the downward force whose magnitude /w is equal to that of upward force that must be applied to the object to hold it at rest or at constant velocity relative to the earth. The direction of weight is in the direction of gravitational force. So the magnitude of weight of an object is denoted as W = N = mg. Note that even though magnitude of weight is equal to mg, it is not same as gravitational force acting on the object. wtsteam100@gmail.com

29) The law of floatation states that a body will float in a liquid, if weight of the liquid displaced by the immersed part of the body is at least equal to or greater than the weight of the body.

30) The average distance travelled by the molecule between collisions is called mean free path (λ) λ = 1 2πd 2 n (or) KT 2πd 2 P (or) m 2πd 2 P λ = 1 2πd 2 n (or) KT 2πd 2 P (or) m 2πd 2 P 1.

5 29) The law of floatation states that a body will float in a liquid, if weight of the liquid displaced by the immersed part of the body is at least equal to or greater than the weight of the body. Ex: The apparent weight of the floating block is equal to zero because the weight of the block acting vertically downwards is balanced by the buoyant force acting on the block upwards. 30) The average distance travelled by the molecule between collisions is called mean free path (λ) λ = 1 2πd 2 n (or) KT 2πd 2 P (or) m 2πd 2 P λ = 1 2πd 2 n (or) KT 2πd 2 P (or) m 2πd 2 P 1. Mean free path increases with increasing temperature. As the temperature increases, the average speed of each molecule will increase. It is the reason why the smell of hot sizzling food reaches several meter away than smell of cold food. 2. Mean free path increases with decreasing pressure of the gas and diameter of the gas molecules. wtsteam100@gmail.com

31) After a systematic study, Wiener and Gouy proposed that Brownian motion is due to the bombardment of suspended particles by molecules of the surrounding fluid.

In the year 1905, Einstein gave systematic theory of Brownian motion based on kinetic theory and he deduced the average size of molecules.

This leads to the motion of the particles in a random and zig In 1827, Robert Brown, a botanist reported that grains of pollen suspended in a liquid moves randomly from one place to other.

6 31) After a systematic study, Wiener and Gouy proposed that Brownian motion is due to the bombardment of suspended particles by molecules of the surrounding fluid. But during 19th century people did not accept that every matter is made up of small atoms or molecules. In the year 1905, Einstein gave systematic theory of Brownian motion based on kinetic theory and he deduced the average size of molecules. According to kinetic theory, any particle suspended in a liquid or gas is continuously bombarded from all the directions so that the mean free path is almost negligible. This leads to the motion of the particles in a random and zig In 1827, Robert Brown, a botanist reported that grains of pollen suspended in a liquid moves randomly from one place to other. The random (Zig - Zag path) motion of pollen suspended in a liquid is called Brownian motion. In fact we can observe the dust particle in water moving in zag manner as shown in Figure. But when we put our hand in water it causes no random motion because the mass of our hand is so large that the momentum transferred by the molecular collision is not enough to move our hand. random directions. This discovery puzzled scientists for long time. There were a lot of explanations for pollen or dust to move in random directions but none of these explanations were found adequate. 32) Laws of simple pendulum i) Law of length: For a given value of acceleration due to gravity, the time period of a simple pendulum is directly proportional to the square root of length of the pendulum T α l ii) Law of acceleration: For a fixed length the time period of a simple pendulum is inversely proportional to square root of acceleration due to gravity T α 1 g iii) The time period of oscillation is independent of mass of the bob and amplitude of oscillation. wtsteam100@gmail.com

33) When the source and the observer are in relative motion with respect to each other and to the medium in which sound propagates, the frequency of sound wave observed is different from the

7 33) When the source and the observer are in relative motion with respect to each other and to the medium in which sound propagates, the frequency of sound wave observed is different from the frequency of the source. This phenomenon is called Doppler Effect. The frequency perceived by the observer is known as apparent frequency. It may be less than or greater than the actual frequency emitted by the sound source. The difference depends on the relative motion between the source and observer

gfjp IV / Part IV 34) Principle of homogeneity of dimensions The principle of homogeneity of dimensions states that the dimensions of all the terms in a physical expression should be the same.

This method is used to i) Convert a physical quantity from one system of units to another. ii) Check the dimensional correctness of a given physical equation.

8 gfjp IV / Part IV 34) Principle of homogeneity of dimensions The principle of homogeneity of dimensions states that the dimensions of all the terms in a physical expression should be the same. For example, in the physical expression v 2 = u 2 + 2as, the dimensions of v 2, u 2 and 2 as are the same and equal to [L 2 T -2 ]. This method is used to i) Convert a physical quantity from one system of units to another. ii) Check the dimensional correctness of a given physical equation. iii) Establish relations among various physical quantities. To convert a physical quantity from one system of units to another This is based on the fact that the product of the numerical values (n) and its corresponding unit (u) is a constant. i.e, n [u] = constant (or) n 1 [u 1 ] = n 2 [u 2 ]. Consider a physical quantity which has dimension a in mass, b in length and c in time. If the fundamental units in one system are M 1, L 1 and T 1 and the other system are M 2, L 2 and T 2 respectively, then we can write,n 1 [M 1 a L 1 b T 1 c ] = n 2 [M 2 a L 2 b T 2 c ]. We have thus converted the numerical value of physical quantity from one system of units into the other system. Let OA is position vector of particle has length 1m and makes 30 with the x - axis. In attachment it is clearly shown in figure OB is the component of OA along x axis. and OD is the component of OA along y - axis. In OAB, Apply, cos30 = OB/OA OB = OAcos30 = 1 3/2 = 1.732/2 = m Similarly, sin30 = AB/OA AB = OD So, sin30 = OD/OA OD = OAsin30 = 1 1/2 = 0.5 m Hence, component of OA along x- axis = m Component of OA along y-axis = 0.5 m wtsteam100@gmail.com

9 35) W = இடப ப யர ச ச வ ச வ ச = வ ச = 30 N இடப ப யர ச ச = 10 m W = 10 m 30 N = 300J we know that w = displacement force so, here work done = force = 30N displacement = 10m W = 10 m 30 N = 300J wtsteam100@gmail.com

10 36)

Case 1: If r < r : The mass m 2 is attracted by m 1 and it can move from r to r without any external work. Work is done by the system and it spends its internal energy.

11 Case 1: If r < r : The mass m 2 is attracted by m 1 and it can move from r to r without any external work. Work is done by the system and it spends its internal energy. Hence work done is said to be negative. Case 2: If r > r : work has to be done against gravity to move m 2 and m 1 from r to r. Work is done on the system by external force. Hence work done is positive. If r =, U ( r) = 0, W = = - Gm 1m 2 r. The gravitational potential energy of a system of two masses m 1 and m 2 separated by a distance r is defined as the amount of work done to bring the mass m 2 from infinity to a distance r assuming m 1 The gravitational force is a conservative force. Consider a mass m 1 fixed in its psition the position vector of mass m 2 is r. Let m 2 be moved through a small distance dr. Work done dw to be fixed in its position. U(r) = - Gm 1m 2. It is r always negative. it is a scalar quantity. Its unit is joule. Its dimensions are ML 2 T 2. = F ext. dr. The work is done against the gravitational force. Hence F ext. = F G = Gm 1m 2, dw = Gm 1m 2 r. dr = Gm 1m 2 dr r 2 r 2 r 2 The total work done for displacing m 2 from r to r is r W = dw = r U(r) - U(r ) r Gm 1m 2 r dr = r 2 ( Gm 1m 2 r r Gm ) = - 1 m 2 + Gm 1m 2 = r r r wtsteam100@gmail.com

12 37) Volume stress = σ n = F n = P, Change in A pressure. Volume strain = ε v = V V Bulk modulus K = - σ n = P ε V v V The negative sign means that when pressure is applied on the body, its volume decreases. Its unit is Nm 2 (or) Pascal. Gases have small value of bulk modulus than solids. Compressibility: the reciprocal of the bulk modulus is called compressibility. It is defined as the fractional change in volume per unit increase in pressure. There are three types of elastic modulus (a) Young's modulus (b) Bulk modulus (c) Rigidity modulus a) Young's modulus: when a wire is stretched or compressed, then the ratio between tensile stress and tensile strain is defined as Young's modulus. Young's modulus = Y = σ t ε t Tensile stress (or)compressive stress Tensile strain (or)compressive strain (or) Y = σ c ε c. S.I. Unit of Young's modulus is Nm 2 (or) Pascal. b) Bulk modulus: Bulk modulus is defined as the ratio of volume stress to the volume strain. Bulk modulus K = Volume stress Volume strain Compressibility C = 1 K = ε v σ n = V V P Since, gases have small value of bulk modulus than solids, their values of compressibility is very high. C) Rigidity modulus: η R = Shearing stress angle of shear (or) shearing strain Shearing stress σ S = tangential force area over which it is applied = F t A The angle of shear or shearing strain ε s = x h = θ Rigidity modulus η R = σ Ft s = A x = ε s h F t A(θ) S.I. unit of rigidity modulus is Nm 2 (or) Pascal. wtsteam100@gmail.com

15 38) 1. All the molecules of a gas are identical, elastic spheres. 2. The molecules of different gases are different. 3. The number of molecules in a gas is very large and the average separation between them is larger than size of the gas molecules. 4. The molecules of a gas are in a state of continuous random motion. 5. The molecules collide with one another and also with the walls of the container. 6. These collisions are perfectly elastic so that there is no loss of kinetic energy during collisions. 7. Between two successive collisions, a molecule moves with uniform velocity. 8. The molecules do not exert any force of attraction or repulsion on each other except during collision. The molecules do not possess any potential energy and the energy is wholly kinetic. 9. The collisions are instantaneous. The time spent by a molecule in each collision is very small compared to the time elapsed between two consecutive collisions. 10. These molecules obey Newton s laws of motion even though they move randomly. wtsteam100@gmail.com

attached to it. One end of the string is connected to a hook and the other end is connected to a weight hanger through a pulley as shown in figure.

Two adjustable wooden knives are put over the board and their positions adjusted to change the vibrating length of the stretched wire.

In between the knife edges, anti-nodes are formed Sono means sound related, and sonometer implied sound related measurements.

16 attached to it. One end of the string is connected to a hook and the other end is connected to a weight hanger through a pulley as shown in figure. Since only one string is used, it is also known as monochord. The weights are added to the free end of the wire to increase the tension of the wire. Two adjustable wooden knives are put over the board and their positions adjusted to change the vibrating length of the stretched wire. Working: A transverse stationary or standing wave is produced and hence, at the knife edges P and q, nodes are formed. In between the knife edges, anti-nodes are formed Sono means sound related, and sonometer implied sound related measurements. It is a device for demonstrating the relationship between the frequency of the sound produced in the transverse standing wave in a string and the tension, length and mass per unit length of the string. Therefore, using this device, we can determine the following quantities. a) The frequency of the turning fork or frequency of alternating current b) The tension in the string.. c) The unknown hanging mass Construction: The sonometer is made up of a hollow box which is one meter long with a uniform metallic thin string wtsteam100@gmail.com

9 MECHANICAL PROPERTIES OF SOLIDS

9 MECHANICAL PROPERTIES OF SOLIDS Deforming force Deforming force is the force which changes the shape or size of a body. Restoring force Restoring force is the internal force developed inside the body