## Kerala Plus One Physics Improvement Question Paper 2018

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. “Some conservation laws are true for one fundamental force, but not for the others”.

Question 2.

The angle between

a. 45°

b. 90°

c. 60°

d. 180°

Question 3.

Three objects with a mass of 40 kg each are placed in a straight line 50 cm apart. What is the net gravitational force at the center object due to the other two?

Question 4.

Which one of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?

a. a = 5x

b. a = -200 x^{2}

c. a = -5x

d. a = 100 x^{3
}

Question 5.

The stress required to double the length of a wire of Youngs modulus Y is ………………

a. Y/2

b. 2Y

c. Y

d. 4Y

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

Question 6.

A car traveling at a speed 54 km/hr is brought to rest in the 90s. Find the distance traveled by car before coming to rest.

Question 7.

The parallelogram law is used to find the resultant of two vectors. Find the magnitude of the resultant of two vectors in terms of their magnitudes and angle between them.

Question 8.

Select the CORRECT alternative.

a. When a conservative force does positive

work on a body, the potential energy of the body ………………………

- increases
- decreases
- remain unaltered

b. Work was done by a body against friction always results in a loss of its …………..

- kinetic energy
- potential energy

c. The rate of change of total momentum of a system of many-particle systems is proportional to the …………… on the system.

- external force
- a sum of the internal forces

d. The quantity which is conserved in an in an elastic collision of two bodies is ………….

- total kinetic energy
- total linear momentum

Question 9.

A steel wire of length 1.5 m and diameter 25 cm is loaded with a force of 98 N. The increase in the length of the wire is 1.5 × 10^{4} m. Calculate the tensile stress and the fractional change in length of the wire.

Question10.

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

a. State the law of equipartition of energy.

b. Write the average value of energy of a molecule for each vibrational mode.

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

Question 11.

Two parallel rail tracks run north-south. Train A moves north with a speed of 15 m/s and train B moves south with a speed of 25 m/s.

a. What is the velocity of B with respect to A?

b. What is the velocity of the ground with respect to B?

c. What is the velocity of a monkey running on the roof of the train A against its motion (with a velocity of 5 m/s with respect to the train A) as observed by a man standing on the ground?

Question 12.

An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes 7 revolutions in 100s.

a. What is the linear speed of the motion?

b. Is the acceleration vector a constant vector? What is its magnitude?

Question 13.

A car arid a truck have the same kinetic energies at a certain instant while they are moving along two parallel roads.

a. Which one will have greater momentum?

b. If the mass of truck is 100 times greater than that of the car, find the ratio of loci of the truck to that of the car.

Question 14.

A girl rotates on a swivel chair as shown below.

a. What happens to her angular speed when she stretches her arms?

b. Name and state the conservation law applied for your justification.

Question 15.

A solid sphere of mass m and radius, R starts from rest and rolls down along an inclined plane of height h without slipping as shown below.

a. Calculate the kinetic energy of the sphere when it reaches the ground.

b. Find the velocity when it reaches the base.

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

Question 16.

A man jumping out of a slow moving bus falls forward.

a. This is due to

b. Which Newtons law gives the above concept? State the law.

c. What is the net force acting on a book at rest on the table?

Question 17.

To reduce friction and accident by skidding the roads are banked at curves.

a. What is meant by banking of roads?

b. Sketch the schematic diagram of a vehicle on a banked road with friction and mark the various forces.

c. Derive an expression for the maximum safe speed of a vehicle on a banked road with friction.

Question 18.

For a liquid-gas interface, the convex side has a high Pressure than the concave side.

a. Derive an expression for excess pressure inside a drop.

b. Which is better, washing of cloth in cool soap wafer or warm soapy water? Why?

Question 19.

Linear expansion is a change in length of an object with temperature.

a. Write the equation for the coefficient of j linear expansion.

b. Show that the coefficient of volume expansion is thrice its coefficient of linear ex! pension.

c. The absolute zero is ……………………………….

[ 273.15°C, 273.15K, 273.15°F, 0°C]

Question 20.

The simplest example of simple harmonic motion is the oscillations of a simple pendulum.

a. Derive an expression for the period of oscillation of a simple pendulum.

b. In a simple pendulum made of a metallic wire, what will happen to the period when the temperature increases? Give a reason.

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

Question 21.

a. The centripetal force depends on the mass of the body, velocity, and radius of a circular path. Find the expression for the centripetal force acting on the body using the principle of dimensional analysis. (Take constant k= 1)

b. When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72” of an arc. Calculate the diameter of a Jupiter.

Question 22.

Satellites are objects which revolve around the earth.

a. The direction of revolution of a geosynchronous satellite is from

i. east to west

ii. west to east

iii. north to south

iv. south to north

b. Derive an expression for a total energy of an orbiting satellite.

c. What is the magnitude of the angular velocity for a geosynchronous satellite?

Question 23.

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

a. Write Bernoulli’s equation.

b. Find the speed of efflux using Bernoulli’s principle.

c. State Torricelli’s law.

Question 24.

The basic features of a device are schematically represented in the figure below.

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

b. Draw the indicator diagram and label the four processes in the Carnot cycle.

c. A steam engine delivers 5.4 × 108J of work per minute and services 3.6 × 109 J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?

Question 25.

A transverse harmonic wave on a string is described by y (x, t) = 3.0 Sin (36t + 0.018x + p/4)where ‘x’ and ‘y is in cm and’ is ins. The positive direction of’ is from left to right.

a. Is this a traveling wave or a stationary wave? If it is traveling, what are the speed and direction of its propagation?

b. What are its amplitude and frequency?

c. What is the least distance between two successive crests in the wave?

Answers

Answer 1.

True

Answer 2.

90°

Answer 3.

Zero

Answer 4.

c. a = -5x

Answer 5.

Y

Answer 6.

Answer 7.

Answer 8.

a. decrease

b. Kinetic energy

c. externally forced

d. Total linear momentum

Answer 9.

Answer 10.

a. 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 kB is Boltzmann’s constant and T is the absolute temperature of the system.

Answer 11.

Answer 12.

Answer 13.

Answer 14.

a. When the girl stretches her arm, according to a law of conservation of angular momentum the distance from the axis of rotation increases and so a moment of inertia increases and thereby angular speed decreases.

b. When no external torque acts on a system of particles, the angular momentum of the system remains constant.

Answer 15.

Answer 16.

a. Inertia

b. Newton’s First Law of Motion. “Everybody continues in its state of rest or uniform motion in a straight line unless some external unbalanced force acts on it”.

c. Zero

Answer 17.

c. Refer QNo. 23, Page No. 61

Answer 18.

a. Refer QNo. 25 (b), Page No. 61

b. Using hot water usually makes whatever is being treated expand or loosen so the dirt can be released easier. It is because hot water has lower surface tension than cold water(Temperature increases surface tension decreases).

This hot water is able to penetrate easily into the pores and wet the surface. In words, As we move along a streamline, Pressure energy + Kinetic energy + Potential energy, per unit volume = Constant.

Answer 19.

Answer 20.

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 θ 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.

1. Weight mg of the bob acting vertically downwards.

2. The tension along the string T. ResoMng 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 = I, OP = x Restoring force, F = -mg sinθ (restoring force tends to reduce angular displacement θ hence the -ve sign) If the displacement ‘x’ is small compared to ‘f, θ ¡s small hence sinθ = e Restoring force, F = -mgθ

b. As temperature increases the length of pendulum increases due to linear expansion. So the period of pendulum increases.

Answer 21.

a. Let F ∝ m^{a}v^{b}r^{c} or F = K m^{a}v^{b}r^{c} ………(1 where K is a dimensionless constant. Writing the dimensions of various quantities ¡n equation (1), we get

Comparing the dimensions of similar quantities on both sides, we get

This is the required expression for the centripetal force.

Answer 22.

a. West to east

b. The kinetic energy of the satellite in a circular orbit at height h from a surface of the earth with speedy is

The potential energy at distance (R+h) from the center of the earth is

c. A time period of geosynchronous satellite = 24hrs

Answer 23.

In words, As we move along a streamline, Pressure energy + Kinetic energy + Potential energy, per unit volume = Constant.

b.

If the top of the tank is also open to atmosphere, then P = P_{a}

The velocity V_{2} is called velocity of efflux. This is same as the velocity of an object falling freely under gravity through a height h.

c. Torricelli’s theorem states that the speed at which fluid leaves the orifice at the bottom of a reservoir is the same as if an object is falling freely through the same height.

Answer 24.

a. Heat Engine

Answer 25.