## Kerala Plus One Physics Model Question Paper 1

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.

Answer any four questions from question numbers 1 to 5. Each carries one score.

Question 1.

State TRUE or FALSE, “weak nuclear force is the weakest fundamental force.

Question 2.

Two vectors \(\bar { A }\) and \(\bar { B }\) are such that \(\left| \bar { A } \times \bar { B } \right| =\bar { A } ,\bar { B }\) Then the angle between the two vectors is ……………

a. 45°

b. 90°

c. 60°

d. 180°

Question 3.

A satellite is revolving around the earth with a kinetic energy E. The minimum addition of kinetic energy needed to make its escape from its orbit is ………………………

Question 4.

A particle executing SHM is an example of

- acceleration of constant magnitude and direction.
- acceleration of changing magnitude and direction.
- acceleration of changing magnitude but constant direction.
- acceleration of constant magnitude but changing direction.

Question 5.

The young’s modulus Young’smaterial of a wire is equal to the

a. The stress required to increase its length four times

b. The stress required to produce unit strain

c. The strain produced in it

d. half the strain produced in it

Answer any four questions from question numbers 6 to 10. Each carries two scores.

Question 6.

When brakes are applied on a moving vehicle, it stops after traveling a distance. This distance is called stopping distance.

a. Write an expression of stopping distance in terms of initial velocity (u) and retardation (a).

b. If the initial speed is doubled keeping the retardation same, by how much will the stopping distance change?

Question 7.

A parallelogram law helps to find the mag

nitude and direction of the resultant of two forces.

a. State the law.

b. If the magnitude of the two vectors and their results are the same, what is the angle between the two vectors?

Parallelogram

result-

Question 8.

Select the CORRECT alternative.

a. When a force is applied to a moving body, its motion is retarded. Then the work is done; is

- positive
- negative
- zero

b. In the stable equilibrium position, a body has

- maximum potential energy
- minimum potential energy

c. The rate of the kinetic energy versus position vector gives the rate of change of

- momentum
- velocity
- force

d. According to a work-energy theorem, the work done by the net force on a particle is equal to the change in its

- kinetic energy
- potential energy

Question 9.

The wire has an unstretched length of 2.40 m and an area of a cross-section of 3.90 × 10^{-7} m^{2}. Determine Young’s modulus Y of the material.

Question 10.

According to the kinetic theory of gases, gas molecules are always in random motion.

a. State the law of equipartition of energy.

b. What do you mean by ‘mean free path’? Give an equation for the mean free path.

Answer any four questions from question numbers 11 to 15. Each carries three scores.

Question 11.

Acceleration time graph of a body starts from rest as shown below:

a. What is the use of the accelerationtime graph?

b. Draw the velocity time graph using the above graph?

c. Find the displacement in the given interval of time from 0 to 3 seconds.

Question 12.

Ramesh observes the motion of an insect in a circle. He finds that it travels 6 revolutions in an anticlockwise direction for a time of 31.4 sec.

a. Find the angular velocity of the insect?

b. If the insect travels 4 revolutions in the clockwise direction for a time of 8.6 sec. What will be the angular speed averaged over the total time?

Question 13.

A circular racetrack of radius 300 m is banked at an angle of 150. The coefficient of friction between the wheels of a race car and the road is 0.2. Find :

- The optimum speed of the race car to avoid wear and tear on its tires.
- Maximum permissible speed to avoid slipping.

Question 14.

Rotational inertia is the tendency of a rotating body to resist any change in its state of rotational motion.

a. What do you mean by the radius of gyration of a rolling body?

b. The figure shows two different spinning poses of a ballet dancer.

In which spinning pose does the ballet dancer have less angular velocity? Justify! your answer.

Question 15.

A and B are two objects moving with velocities V_{A} and V_{B}?

a. What is the velocity of A relative to B?

b. Rain is falling vertically with a speed of

35 m/s. A woman rides a bicycle with a speed of 12 m/s in the east to west direction. What is the direction in which she should hold her umbrella?

Answer any four questions from question numbers 16 to 20. Each carries four scores.

Question 16.

a. The value of acceleration due to gravity is maximum at the

- Poles
- Equator ;
- Centre of the earth

b. Find the height at which ‘g’ is reduced to g/2. 2 I

c. A rat and a horse are to be projected from earth into space. State whether the veloc ity is the same or different in projecting; each animal. Justify.

Question 17.

A person in an artificial satellite of the earth experiences weightlessness. The moon is a natural satellite of the earth.

a. Can a person on the moon experience weight? Why?

b. A satellite is revolving very close to the earth. What is the percentage increase in velocity needed to make it escape from the gravitational field of the earth?

c. Acceleration due to gravity ‘g’ depends on the distance ‘r’ from the center of the earth. Draw a graph showing the variation of‘g’with r’.

Question 18.

a. A solid sphere falling through a viscous

medium attains a constant velocity called terminal velocity after some time of its fall. What are the different forces acting, on the sphere? Derive an epression for terminal velocity in terms of the coefficient of viscosity of the medium. 3 b. Water kept in earthern pots gets cooled. Why?

Question 19.

Mechanical power is represented by P = FV +

Av3p; where F is the force, v is the velocity; A ! is the area and p is the density.

a. The dimensional formula of power is

b. Check the dimensional validity of the above , equation.

c. Which of the following equations can’t be obtained by the dimensional method?

Question 20.

While conducting a resonance column experiment in the laboratory, you can hear the maximum sound at a certain height.

a. Explain the phenomenon of sound.

b. Show that in a closed pipe at one end, the frequencies of the first three harmonics; are in the ratio of vt: v2: v3 = 1: 3: 5. 2!

c. Open pipes are preferred to closed ones in musical instruments. Why?

Answer any four questions from question numbers 21 to 25. Each carries 5 scores.

Question 21.

Raising the outer edge of a curved road a little above the inner edge is called banking of curves.

a. Derive an expression for the safe speed with which a car can negotiate a banked road by taking into account the friction between the tires and the road.

b. A machine gun fires bullets of mass 40g each with a speed 1200 ms1. The person can hold the gun with a maximum force of 144 N. What is the maximum number of bullets that can be fired per second from the gun?

Question 22.

Earth satellites are objects which revolve around the earth. Consider a satellite at a ‘ height ‘h’ from the surface of the earth.

a. Give an equation for its orbital velocity.

b. Obtain an equation for the period of the above satellite.

c. Distinguish between geostationary satellites and polar satellites.

Question 23.

The pressure of the atmosphere at any point is the weight of the air column of a unit cross-sectional area. Its unit is a bar.

a. Identify the diagram and write its use.

b. State Pascal’s law for transmission of fluid pressure and explain the principles j of working of a hydraulic lift.

c. The above arrangement is placed in an ; elevator which is accelerating upwards, i What happens to the possible height of ; the liquid column in the tube? Justify.

Question 24.

Aheatengineisadevicewhichconvertsheatenergy into work.

a. What is the working substance in an ideal heat engine?

b. Draw the Carnot cycle and explain its working.

c. Calculate the efficiency of an engine working between steam point and ice point.

Question 25.

a. Wave motion is the propagation of energy through a material medium due to repeated periodic motion.

- Transverse waves cannot be propagated through gases. Why?
- What was the condition assumed by Laplace in correcting Newton’s equation for the velocity of sound in a gas? Write the newton Laplace equation.

b. A source of the sound of frequency 256 Hz is in between a listener and a wall. If the source is moving towards the wall with a velocity of 5ms1, how many beats per second will be heard if the sound travels with a speed of 330ms’1?

Answers

Answer 1.

False. Gravitational force is the weakest fundamental force.

Answer 2.

45°

Answer 3.

E

Answer 4.

2

Answer 5.

The stress required to produce unit strain

Answer 6.

a. When vehicle comes to rest v = 0, a = a

substituting these values in

b. When a body comes to rest, work is done = change in kinetic energy

The stopping distance becomes 4 times the original distance.

Answer 7.

a. Parallelogram 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.

b. R = A + B + 2AB cosθ

Answer 8.

a. negative

b. minimum potential energy

c. momentum

d. kinetic energy

Answer 9.

[slope from graph may vary slightly and mark may be granted to possible correct answers irrespective of variations.]

Answer 10.

Law of equipartition energy:

It states that in any dynamical system in thermal equilibrium, the energy is equally distributed amongst its various degrees of freedom and the energy associated with each degree of freedom per molecule is 1/2k_{B}T, where k_{B} is Boltzmann’s constant and T is the absolute temperature of the system.

b. The average distance traveled by the molecules between two successive collisions is called the mean free path. Mean free path \(=\frac { l }{ \sqrt { 2n\pi { d }^{ 2 } } }\) (‘n’ is the number of molecules per unit volume’ is the diameter of the molecule).

Answer 11.

a.

- The area of the acceleration time graph gives change in velocity.
- From a 1 graph, we can find instantaneous acceleration.
- Slope of a 1 graph gives rate of change of acceleration.

c. Displacement = Area under graph

= Area of DOAB

= 14 × 3 × 12 = 18m

Answer 12.

a. Angular velocity \(\omega =\frac { 2\pi n }{ t } =\frac { 2\pi \times 6 }{ 3.14 } =1.2rad/s\)

b. Period of rotation in clockwise,

Answer 13.

Answer 14.

a. A radius of gyration of a body about an axis of rotation is defined as the distance from the axes to a point at which the whole mass of the body is assumed to be concentrated. It is denoted by K. \(K\sqrt { \frac { I }{ M } }\)

b: Fig (a), in this pose, a moment of inertia is larger than the fig (b).

Answer 15.

Answer 16.

a. Poles

b. Let ‘h’ be the height from the surface of the earth where the value of g is g/2.

c. Velocity is same ie, V_{e} = \(\sqrt { 2gR }\) Escape velocity is independent of the mass of the body that projected into space.

Answer 17.

a. Yes. Moon attracts every body towards its center.

b. Orbital velocity V_{0} = \(\sqrt { Rg }\)

Escape velocity V_{e} = \(\sqrt { 2Rg } =\sqrt { 2 } { V }_{ 0 }\) % change in velocity

18. a. The forces acting on the sphere are

- The weight of the sphere acting downward
- A viscous force acting upward
- Buoyant force acting upward.

An expression for terminal velocity:

Consider a small sphere of radius Y and mass placed on a surface of a highly viscous liquid contained in a jar. According to Stoke’s formula, a viscous force on the sphere moving with a terminal velocity ‘V and radius Y is given by F = 6πrnv where ‘n’ is the coefficient of viscosity of the fluid. Apparent weight of the sphere in a fluid is [ltex]\frac { 4 }{ 3 } \pi { r }^{ 2 }pg-\frac { 4 }{ 3 } \pi { r }^{ 3 }og[/latex]Where p is the density of the material of sphere a and that of the liquid At terminal velocity, \(\frac { 4 }{ 3 } \pi { r }^{ 3 }\left( p-\sigma \right)\)

b. Due to evaporation.

Answer 19.

Answer 20.

a. If a wave is produced at the open end of a tube it travels through the gas column and gets reflected at the closed end. At a certain height of tube the incident wave and reflected wave superpose each other and produce stationary wave and a sound is heard. This is called resonance. The open end always represents an antinode.

b. The first normal mode of vibration

Let l_{1} be the wave length of standing have set up in the pipe corresponding to

The second normal mode of vibration (3rd harmonic, 1st overtone)

Let λ_{2} be the wavelength of standing wave set up in the pipe corresponding to n = 2

Let λ_{3} be the wave length of standing wave set up in the pipe corresponding to n = 3

The ratio of the first, second and third mode. V_{1 }: V_{2} : V_{3} = 1 : 3 : 5

c. All harmonics are present in open pipe, but in the closed pipe, only odd harmonics are present. So open pipe is preferred in a musical instrument.

Answer 21.

Let ‘mg’ be the weight of a vehicle moving with a speed ‘V around a banked road of radius ‘r’. Its normal reaction ‘ R’ can be resolved into 2 component R cos0 vertically upwards and R sinq towards the center of the curve. R sin0 gives necessary centripetal force while R cos0 balances the weight ‘mg’.

The direction of the frictional force Fs is such that the force resists the tendency of the car to skid to the outside of the curve. The horizontal component Fs cos0 is added to R sinq to provide a large centripetal force.

Substituting the value of R in equation (2)

divide the numerator and denominator by cosθ

Answer 22.

c. Satellite in a circular orbit of radius about 36,000 km around the earth in the equatorial plane with T = 24 hours is called geostationary satellites. They are mainly used for communication purpose, TV and Radio broadcasting and Weather forecasting.

Polar satellites are low altitude satellites that go around the poles of the earth in a north-south direction. Its time period is around 100 minutes and so it crosses any altitude many times a day. Its height above the earth is about 500800 km. In formation gathered from such satellites is extremely useful for remote sensing, meteorology as well as for environmental studies of the earth.

Answer 23.

a. Mercury barometer.

b. Pascal law. It states that an increase in pressure at one point of the enclosed liquid at rest is transmitted equally to every part of the liquid and to the wall of the container provided the effect of gravity is neglected.

In a hydraulic lift, two pistons are separated by the space filled with a liquid. A piston of small cross section A_{1} is used to exert a force F_{1} directly on the liquid. The pressure is P = \(\frac { { F }_{ 1 } }{ { A }_{ 1 } }\) is transmitted throughout the liquid to the larger cylinder attached with a larger piston of area A_{2}, which results in an upward force of P x A_{2}. Therefore, the piston is capable of supporting a large force (large weight of, say a car, or a truck, placed on the platform) F_{2} = PA_{2} = \(\frac { { F }_{ 1 }{ A }_{ 1 } }{ { A }_{ 1 } }\) By changing the force at A1, the platform can be moved up or down. Thus, the applied force has been increased by a factor of \(\frac { { A }_{ 2 } }{ { A }_{ 1 } }\) and this factor is the mechanical advantage of the device. The example below clarifies it.

c. Decreases, because of g decreases OR (g’ = g – a)

Answer 24.

a. Ideal gas or perfect gas

Carnot engine is an ideal heat engine. Main parts of Carnot engine are a source, working substance is an ideal gas which taken in a cylinder provided with a piston. The 3 sides of the cylinder are an insulator and the lower side is conducting, sink and an insulated stand. Adiabatic process in a car not cycle is performed in this insulated stand.

The four stages of the cycle are:

1. Isothermal expansion The cylinder containing the gas is placed in thermal contact with the source kept at high temperature (T_{1},), It absorbs Q_{1} amount of heat and expands, the expansion is isothermal. The initial pressure p_{1} and volume V_{1} of the gas change to p_{2} and V_{2}. Thus the gas does a work W_{AB}

2. Adiabatic expansion (BC) The gas is placed on an insulating stand. Now no heat enters or leaves the system, the expansion is adiabatic. Pressure and volume change from p_{2} and p_{3} and V_{2} to V_{3}. During the process, temperature falls to T_{2}. Work done by the gas is WBC.

3. Isothermal compression (CD) The cylinder is then placed on the sink at temperature T_{2}. Gas is compressed to reject some heat Q_{2} to the sink. Since temperature T_{2} remains constant, the compression is isothermal. Pressure and volume changes to p_{4} and v_{4} work done on the gas is WCD.

4. Adiabatic compression. The cylinder is again placed on the insulating stand for the completion of the compression process. Since no heat transfers or leaves the system, the compression is adiabatic. The gas attains the original pressure p_{1} and volume v_{1} at the end of this. Work done now is WDA.

Answer 25.

a.

i. Modulus of elasticity of gas is zero.

ii. Laplace corrected Newtons formula taking condensation and rare fraction as adiabatic process, v = \(\sqrt { \frac { VP }{ p } }\)