## Kerala Plus One Physics Model Question Paper 3

Time: 2 Hours

Cool off time: 15 Minutes

Maximum: 60 Scores

General Instructions to candidates

- There is a ‘cool off time’ of 15 minutes in addition to the writing time.
- Use the ‘cool off time’ to get familiar with the questions and to plan your answers.
- Read the instructions carefully.
- Read questions carefully before you answering.
- Calculations, figures, and graphs should be shown in the answer sheet itself.
- Malayalam version of the questions is also provided.
- Give equations wherever necessary.
- Electronic devices except non-programmable calculators are not allowed in the Examination Hall.

Questions 15 carry 1 score each. Answer any I four questions.

Question 1.

The branch of Physics which deals with the study of phenomena related to light.

a. Optics

b. Thermodynamics

c. Mechanics

d. Electronics

Question 2.

State the theorem of perpendicular axes on a moment of inertia.

Question 3.

Select a true statement from the following.

a. The distance traveled by light in one year through vacuum or air is an astronomical unit.

b. The range of time in Physics varies from 10^{-14} sec to 10^{-25} sec.

c. Lightyear is the largest practical unit of length.

d. Chandra Shekhar Limit (C.S.L) is the largest practical unit of mass.

Question 4.

When two objects collide, after collision they could move together, the collision is ……………………

(elastic, completely elastic, inelastic, completely inelastic)

Question 5.

List any two conditions for a motion of a body to be simple harmonic.

Questions 6 to 11 carry 2 scores each. Answer any 5 questions.

Question 6.

The possibility of falling backward with the ladder is more when you are high up on the ladder than when you just begin to climb. Explain why.

Question 7.

The displacement of y (in cm) of an oscillating particle varies with time t (in a sec) according to the equation. y = 2 cos (0.5 πt + π/3) Find the amplitude and period of the particle

Question 8.

Draw the stress-strain graph of a loading wire. Mark the following points:

- Elastic limit
- Fracture point
- Plastic region
- Elastic region.

Question 9.

Calculate the work done in lifting a body of mass 10 kg to a height of 10 m above the ground. 10 kg

Question 10.

a. Which among the following possess the highest specific heat capacity?

- Water
- Silver
- Copper
- Steel

b. You are in a restaurant waiting for your friend and ordered coffee. It has arrived. Do you add sugar to your friend’s coffee and then wait for him or do you add sugar after he arrives? Explain with respect to the concept of cooling.

Question 11.

A collision between two particles need not be the physical contact of two particles as in the case of scattering of the particle by a nucleus.

a. What is the quantity that remains conserved in all types of collisions?

b. Suppose an electron and a proton are projected with equal kinetic energy, What will be the ratio of their linear momentums if the proton is 1830 times heavier than an electron?

Questions 12 to 17 carry 3 scores each. Answer any five questions.

Question 12.

Motion along a plane is called two-dimensional motion. A body moving in two dimensions is found to have an acceleration in one dimension.

a. Identify the motion.

b. A ball thrown by a player reaches another player in 2s. What is the maximum height attained by the ball above the point of projection? (Take g= 10ms^{-2})

c. In the figure, the point P on a wheel of radius R is in contact with the ground. What is the displacement of the point, when the wheel rolls a half revolution?

Question 13.

All physical quantities can be expressed in terms of dimension.

a. Write the physical quantities of the following dimensions:

i. [M^{1}L^{1}T^{1} ]

ii. [M^{2}L ^{2}T^{2}]

b. Check whether the equation T = \(T=2\pi \sqrt { \frac { m }{ g } }\) is dimensionally correct

T → Time period of a simple pendulum

m → mass of the bob

g → acceleration due to gravity

Question 14.

Kinetic theory of gases is based on the molecular picture of matter.

a. Write any two postulates of kinetic theory of gases.

b. Write short notes on:

- Equipartition of energy
- Mean free path

Question 15.

The stress-strain graph for wires of two materials A and B are given below.

a. Which material is more ductile?

b. When spring balances are continuously used for a long time, they show a wrong reading. Explain why?

Question 16.

Force is required to lift a body from the ground to a height h and work is measured as the product of force and magnitude of displacement.

a. Name the energy possessed by the body at maximum height. Write an equation for it.

b. A man of mass 60 kg carries a stone of mass 20 kg to the top of a multi-story building of height 50m. Calculate the total energy spent by him? (g = 9.8 m/s^{2})

Question 17.

The acceleration due to gravity o,n the surface of the moon is 1.7 m/s^{2}. what is the time period of a simple pendulum on the moon, if its time period on Me earth is 3.5 second?

Questions 18 to 22 carry 4 scores each. Answer any 4 questions.

Question 18.

A stone is thrown with the help of a sling with initial velocity V_{Q} at an angle θ from the horizontal.

a. Working of a sling is based on a law of vector addition.

b. With the help of a vector diagram, state this law.

c. Derive the expression for the maximum height reached by the

Question 19.

The velocity of sound depends on density (p) and modulus of elasticity (E). (The dimensional formula of E is ML^{-1} T^{-2})

a. State the principle of homogeneity.

b. Using the above principle, arrive at an expression for the velocity of sound. (Take K = 1).

Question 20.

Hooke’s law states that stress a strain.

a. What is the necessary condition for the above law to be valid?

b. Explain with the help of a graph, the relation between stress and strain for a given solid material under increasing tensile stress.

Question 21.

a. The figure shows the position-time graph of a body moving along a straight line.

- Draw the velocity-time graph of the body.
- From the graph, find the displacement in 20 seconds.

b. From the velocity-time graph of a body moving with uniform acceleration, deduce the velocity-time relation and the velocity displacement relation.

Question 22.

The motion represented by the equation, y(t) = A cos (ωt + Φ) is called simple harmonic motion (SHM).

a. Which one of the following examples ‘ closely represents SHM? Substantiate your answer.

- The rotation of the earth about its axis.
- Oscillations of a swing.

b. A vibrating simple pendulum of period T is placed in a lift which is accelerating downwards. What is the effect of this on the time period of the pendulum?

Questions from 23 to 26 carry 4 scores. Answer any 3 questions.

Question 23.

According to Newton’s law of motion, the force depends on the rate of change of momentum.

a. Name the law that helps to measure force.

b. Using the above law, deduce an expression for a force.

c. A man jumping out of a moving bus falls with his head forward. What should he do in order to land safely?

Question 24.

The flow of an ideal fluid in a pipe of a varying cross-section is shown.

a. Differentiate between streamline flow and turbulent flow.

b. State and prove Bernoulli’s principle.

Question 25.

The figure given below depicts the schematic representation of an engine.

a. Which type of engine is this, a heat engine or a refrigerator?

b. Write the 4 steps of operation in the Carnot cycle.

c. A Carnot engine is working with a temperature of 27°C and 327°C. Find its efficiency (η).

Question 26.

In a hammer throw event, a solid sphere of mass 16 kg is tied to a light 50 cm long chain. A sportsman gives it a constant moment of 30 Nm for 10 seconds and then throws the sphere. Consider the sphere as a point mass.

a. Find the moment of inertia about the axis of rotation.

b. If ‘L’is the angular momentum and τ is the torque. Show that τ = \(\frac { dL }{ dt }\)

c. Write an example for the motion in which an angular momentum remains constant.

Answers

Answer 1.

Optics

Answer 2.

This theorem is good for flat bodies which means, thickness much less than length and breadth. The theorem states that “the moment of inertia of a plana body about an axis perpendicular to its plane is equal to the sum of moments of inertia about two mutually perpendicular axes passing through the same point, lying on the plane”.

Answer 3.

d

Answer 4.

Completely inelastic.

Answer 5.

1. acceleration is directly proportional to displacement. i.e., a α y

2. Periodic motion.

Answer 6.

As the distance from the axis of rotation (r) increases, the torque also increases. When we are high on the ladder the, r is greater and so a small force in the perpendicular direction can cause a large torque. So there is a greater chance of falling.

Answer 7.

A pendulum whose period is 2 seconds is called seconds pendulum. y = A cos (ωt + ∅)

- x = 20 cos (62.Bt + π/14) Amplitude = 20 icm
- Frequency a> = 62.8
- Initial phase = 14 Strain

Answer 8.

Answer 9.

Work was done = Force × displacement

W = mg × h = 10 × 9.8 × 10 = 980 J

Answer 10.

a. Water.

b. Add sugar as soon as the coffee arrives and then wait. This is Newton’s law of cooling. Thus when sugar is added to coffee, the temperature of coffee decreases. Hence the rate of cooling also decreases.

Answer 11.

a. Momentum is conserved

b. The kinetic energy of an electron

Answer 12.

a. Projectile motion

Answer 13.

a.

- Momentum or impulse
- Work, energy, torque

So the equation is wrong

Answer 14.

a. AverageThe average energy of a molecule of an ideal gas is proportional to the absolute temperature. PV = nRT at all pressure and temperature.

b.

- According to equipartition theorem, total energy of a system is equally distributed among various degree of freedom.
- Mean free. a path is the mean distance traveled by the molecules between two successive collisions.

Answer 15.

a. Material A is more ductile.

b.This is due to a phenomenon known as fatique. Due to continuous use for a long time, the elasticity of materials decreases. So they show a wrong reading.

Answer 16.

a. Potential energy U = mgh

b. m = 60 + 20 = 80 kg;

h = 50m; g= 9.8 m/s^{2}

U= mgh = 80 × 9.8 × 50

= 39200J

Answer 17.

g_{m }= 1.7 m/s^{2}, T_{m} = ? T= 3.5 s

Answer 18.

a. Parallelogram law of vector addition.

b. It states that “if two vectors are represented both in magnitude and direction by the adjacent sides of a parallelogram drawn from a point, then the resultant vector is represented both in magnitude and direction by the diagonal of the parallelogram passing through the same point”.

c. Horizontal range (R). It is the horizontal distance covered by a projectile from the point of projection on the ground to the point on the ground where the projectile returns again. R = horizontal velocity x time of flight (The horizontal velocity v cosQ of the projectile will be a constant)

The above equation shows that R is maximum when sin 20 is maximum, ie., when 0 = 45°

The maximum horizontal range Rmax = \({ R }_{ max }=\frac { { u }^{ 2 } }{ g }\)

Answer 19.

a. Acca ordering to a principle of homogeneity, the dimensions of the same fundamental quantity must be the same on both sides of the equation.

Answer 20.

a. Hooke’s law states that within elastic limit stress is directly proportional to strain.

Consider a uniform wire suspended freely from a fixed point. The face end is subjected to a stress and strain is noted. In the above graph, stress is on Y-axis, and strain on X-axis.

In the initial stages as stress increases strain also increases linearly from 0 to A. Till A stress a brain. For the all-region AB the proportionality is lost but even in this region, the wire will partially recover its initial state.

Beyond B (B is called the elastic limit). The strain increases very rapidly and it is seen that the wire retains the law dimension’s on the removal of the force. Now its behavior is plastic.

Beyond this point, even without increasing the stress any further the wire extends and ultimately at D, it breaks. This point D is called Breakpoint or yield point.

Answer 21.

a. A slope of a displacement-time graph (x-t) gives velocity. Velocity in the interval 0 – 5 sec.

When we draw a velocity-time graph, we get a graph as shown in the figure

ii. An area under the velocity-time graph gives displacement. Area A = 2 × 5 + 2 × 5 = 0 displacement = 0

b. Consider a body moving with uniform acceleration ‘a’. Let u be the initial velocity at a time t = 0 and v be the final velocity at time t.

But from equation (1), we get t = \(\frac { v-u }{ a }\)

Answer 22.

a. A simple harmonic motion is special type of motion which is periodic and takes place continuously at regular intervals of time in which a body moves to and fro on a straight line about a fixed point under a restoring force which is directed always towards the fixed point and directly proportional to displacement at that instant from the fixed point.

An ideal simple pendulum is made of a heavy point mass body suspended from rigid support by an inextensible, weightless and perfectly flexible string. The body is free to oscillate in a vertical plane. When an undisturbed pendulum is in the position ‘SO’. ‘S’ is the point of suspension and ‘O’ is the center of gravity of the bob.

The position SO is the equilibrium position. If the bob is slightly pulled aside and released, the pendulum oscillates between Q and P. Q & P represents the position of a center of gravity of the bob in the displaced position during the oscillation, then the force at P is shown in the figure.

- Weight, mg of the bob acting vertically downwards.
- The tension along the string T.

Resolving mg we get mg sinθ and mg cosθ as shown in the figure. Here mg cosθ balances the tension and mg sinθ acts tangentially at P hence it acts as the restoring force.

Let SO = SQ = SP = L

Let OP = x

Restoring force F = mg sin θ (Restoring force tends to reduce angular displacement θ hence the ve sign).

If the displacement ‘x’ is small compared to 1 θ is small hence sinθ = θ Restoring force F = – mg θ

Answer 23.

a. Newton’s 2^{nd} law of motion.

b. The law state that the rate of change of linear momentum is directly proportional to the applied force and it takes place in the direction of applied force. According to the second law,

c. A man jumping out of a moving bus falls with his head forward because his body gets a forward momentum and has a tendency to continue in the state of motion (inertia of motion) so in order to land safely he should not stand stationary but continue in the state of motion by running for a while.

Answer 24.

a. Streamline flow is defined as a flow in which all the liquid particles that pass any given point follow the same path at the same speed.

When the velocity of flow exceeds the critical velocity, the flow becomes Turbulent. The flow of a liquid is said to be turbulent flow if the speed and direction of the liquid particles passing any point change with time.

b. According to Bernoulli’s theorem, the steady flow of an ideal liquid, the total energy per unit volume remains constant throughout the flow. France by Bernoulli’s theorem, kinetic energy + potential energy + pressure energy = a constant throughout the flow

Consider the steady flow of a liquid through a nonuniform tube as shown in the figure. The pressure area of cross-section and speed at A are P_{1}, a_{1}, v_{1} and P_{2}, a_{2}, v_{2}, at B. A and B are at height h_{1} and h_{2} from the horizontal. Let in time at liquid near

Total energy at A = Total energy at B Thus Bernoulli’s Theorem is proved.

Answer 25.

Heat engine.

Adiabatic expansion → BC

Isothermal compression → CD

Adiabatic compression → DA

c. The efficiency of a Carnot engine working between two temperature T_{1 }and T_{2 }of hot and cold reservoir is given by

Answer 26.

c. A motion of the earth around the sun.