## Kerala Plus One Physics Model Question Paper 4

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.

Engineering Physics MCQ with answers in PDF format.

Question 1.

Name the weakest force among the fundamental forces.

Question 2.

The work done during an isochoric process is …………….

The harmonic sequence formula is a sort of average calculator that is estimated by dividing the number of utilities.

Question 3.

Highway police detect over speeding vehicles by using ……………….

a. Magnus effect

b. Pascals law

c. Doppler effect

d. Bernoulli’s theorem

Question 4.

Two forces 3N and 4N are acting perpendicular to each other. The magnitude of the resultant force is

Question 5.

Say true/false: “Trade winds are produced due to conduction.”

Answer any five questions from question numbers 6 to 11. Each carries two scores.

Question 6.

The displacement (S) of a body in time ‘t’ is given by S = at^{2} + bt. Find the dimensions of a and b.

Question 7.

Give the magnitude and direction of the net force on a stone of mass 0.1 kg.

a. Just after it is dropped from the window of a train accelerating 1 ms^{2}.

b. Lying on the floor of a train which is accelerating with 1 ms^{-2}, the stone being at rest relative to the train.

Question 8.

A body is rolling on a horizontal surface. Derive an equation for its kinetic energy,

Question 9.

The stress-strain graphs for two materials A and B are shown below (the graphs are drawn using the same scale) Which one is more elastic? Why?

Question 10.

“A heavy and a light body have the same kinetic energy.” Which one has greater momentum? Why?

Question 11.

The following figures refer to the steady flow of a nonviscous liquid. Which of the two figures is correct? Why?

Answer any five questions from question num 1.5 m numbers 12 to 17. Each carries three scores.

Question 12.

The side of a cube is measured as 3.405 cm.

a. How many significant figures are there in the measurement?

b. If the percentage error in the measurement of the side of the cube is 3%, find; the percentage error in its volume.

Question 13.

According to the conservation of energy “energy can neither be created nor be destroyed”

a. Prove law of conservation of mechanical energy in the case of a freely falling body.

b. The bob of a pendulum of length 1.5 m is released from the position A shown in the figure. What is the speed with which the bob arrives at the lowermost point B, given that 5% of its initial energy is dissipated against air resistance?

Question 14.

Acceleration due to gravity on earth changes with depth and height.

a. What is the weight of a body placed at the center of the earth? Why?

b. Find the height at which the acceleration due to gravity is 1/4^{th} that at the surface of the earth.

Question 15.

A metal sphere of density ‘p’ and radius ‘a is falling through an infinite column of liquid of density ‘o’ and coefficient of viscosity Ty

a. Name any two forces acting on the; sphere.

b. With the help of Stokes theorem, derive an equation for the terminal velocity of I the sphere.

Question 16.

Conduction is the mode of transfer of heat in solids. of Write the unit of thermal conductivity.

b. “Burns produced by steam is severe than that produced by boiling water”Why?

Question 17.

A gas has ‘f’ degrees of freedom.

a. Calculate its Cp, Cv, and γ.

b. Define the mean free path.

Answer any five questions from question numbers 18 to 22. Each carries two scores.

Question 18.

A satellite moves in a circular orbit of radius ‘r’ with an orbital velocity.

a. Derive an equation for the orbital velocity of a satellite.

b. The time taken by Saturn to complete one orbit around the Sun is 29.5 times the earth year. If the distance of the earth from the Sun is 1.5 × 108km, then what will be the distance of the Saturn from the Sun?

Question 19.

In the simple harmonic motion, force is directly proportional to the displacement from the mean position.

a. Give an example of a harmonic oscillator.

b. Derive equations for the kinetic and potential energies of a harmonic oscillator.

c. Show graphically the variation of kinetic energy’ and potential energy of a harmonic oscillator.

Question 20.

A stretched string can be used as a musical instrument.

a. What is the fundamental frequency of a stretched string?

b. With neat diagrams, derive equations for the second and third harmonics of a stretched string.

Question 21.

A body having an initial velocity ‘v_{0}’ has an acceleration ‘a’.

a. Using the velocity-time graph, derive an equation for displacement of the above body.

b. Draw the velocity Time graph and speed Time graph of a body thrown vertically in the air.

Question 22.

A javelin is thrown with an initial velocity ‘ V_{0}‘ at an angle ” with the horizontal.

a. What are the horizontal and vertical velocities of the body

i. At the point of projection

ii. At maximum height

b. Find the angle of projection at which the maximum height attained by the javelin is equal to the horizontal range.

Answer any three questions from question numbers 23 to 26. Each carries five scores.

Question 23.

a. What is meant by ‘banking of roads’?

b. With a neat diagram, derive an equation for the maximum velocity of a car on a banked road.

c. What is the optimum speed of the car along the banked road?

Question 24.

The moment of inertia of a thin rod of mass M and length 1 about an axis perpendicular to the rod at its midpoint is \(\frac { { Ml }^{ 2 } }{ 12 }\).

a. What is the radius of gyration in the above case?

b. A student has to find the moment of inertia of the above rod about an axis (AB) perpendicular to the rod and passing through one end of the rod. Name and state the law used for this case.

c. Using the theorem, find the moment of inertia of the rod about AB.

Question 25.

Small drops of water assume spherical shape due to surface tension.

a. Define surface tension.

b. Derive an equation for the excess pressure inside a liquid drop of radius ‘R’ having surface tension σ.

c. Why do farmers plow the fields before summer?

Question 26,

Carnot engine is considered as an ideal heat engine.

a. Draw the PV graph of Carnot’s cycle.

b. Derive an equation to find the work done during an adiabatic process.

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

Answers

Answer 1.

Doppler effect

Answer 2.

Zero

Answer 3.

Doppler effect

Answer 4.

7N

Answer 5.

False

Answer 6.

[S] = [L]

[at^{2}] = [L]

a = [LT^{-2}]

[bt] = [L]

[b] = [LT^{-1}]

Answer 7

a. Only force is gravitational. F = mg = 0.1 × 9.8 = 9.8 N downward j

b. Gravitational force is cancelled by normal I reaction.

∴ F_{2} = ma = 0.1 × 1 = 0.1 N, direction of motion of train.

Answer 8.

Answer 9.

In the two graphs, the slope of a graph of material A is greater than the slope of a graph of material B. So material A is more elastic than B. For material A the break-even point (D) is higher.

Answer 10.

Momentum is greater for a heavy body.

Answer 11.

Figure b is correct. According to an equation of continuity, the speed of liquid is larger at a smaller area. From Bernoulli’s theorem due to larger speed, the pressure will be lower at a smaller area and therefore the height of liquid column will also be at lesser height, while in Fig(a) height of liquid column at the narrow area is higher.

Answer 12.

Answer 13.

a. Law of conservation of energy. Energy can neither be created nor be destroyed, but it can be transformed from one form into another. Consider a body of mass’s’ placed at

b. Changing in PE after dissipation.

Answer 14.

Answer 15.

a. i. Weight, F, = mg acting downward

ii. Viscous force, F2 acting upward,

b. By strokes, formula F = 6πrηV Viscous force = Apparent weight of sphere in the solid

Answer 16.

a. W m^{-1}K^{-1}

b. Boiling water contains only a specific amount of heat energy required for it to boil. However, as steam is formed from boiling water, it contains the heat energy of boiling water, along with the latent heat of vaporization.i.e., 1kg of steam at 100°C contains 22.6 × 10^{5} J more heat than 1 kg of water at 100°C. Hence, as steam has more heat energy, it can cause more severe burns than boiling water.

Answer 17.

b. Mean free path is an average distance between two successive collisions.

Answer 18.

a. It is the velocity required to put the satellite into its orbit around the earth.

The gravitational force on the satellite

The centripetal force required by the satellite to stay in this orbit is

in this orbit is In equilibrium the centripetal force is given by the gravitational force

Answer 19.

a. Oscillation of simple pendulum Oscillation of loaded spring

b. Let m be the mass of the particle executing SHM. Let v be the velocity at any instant,

Potential energy is the work required to take a particle against the restoring., force. Let a particle be displaced through a distance x from the mean position. Then restoring force, F = – kx, where k is the force constant. Now if we displace the particle further through a distance dx, Small work done, dw = – Fdx = kx dx Total work done from 0 to x

Answer 20.

a. Fundamental mode (or) First harmonic: If the string is plucked in the middle and released, then it vibrates in one segment with nodes at its ends and an antinode in the middle.

This is the lowest frequency with which string vibrates.

b. Second harmonic If the string is pressed in the middle and plucked at one-fourth of its length, then the string vibrates in two segments.

Third harmonic If the striping is pressed at one-third of its length from one end and plucked at one-sixth its length, it will vibrate in three segments.

Thus a collection of all possible mode is called harmonic series and n is called harmonic number.

Answer 21.

The area under the velocity-time graph gives the displacement of the body. Displacement, x = area OABD x = area of triangle ABC+ area of rectangle OACD.

Answer 22.

a.

i. Horizontal V_{x} = V_{0} cosθ Vertical V_{y} = V_{0}sinθ

ii. Horizontal V’_{x} = VO cosθ

Answer 23.

a. To avoid skidding and damage to tires of vehicles, the outer part of a road is slightly raised than the inner part. This is known as banking of roads.

The forces on the car are:

1. The weight of the car vertically downwards.

2. Normal reaction Racing normal to the road.

3. Frictional force acting parallel to the road.

Since there is no vertical acceleration,

R cosθ = mg + F sinθ

or R cosθ – F sinθ = mg …(1)

Now for maximum speed, F = μ, R

The centripetal force is provided by horizontal components of Rand Fas shown in the figure.

Answer 24.

a. The radius of gyration (k). It is the defined as the distance from an axis of rotation at which, if the whole mass of the body was concentrated, then its moment of inertia about that point would be the same as the moment of inertia of actual distribution of mass. l = Mk^{2}

The radius of gyration (k) of a body is the square root of a ratio of the moment of inertia and a total mass of the body.

ie., a radius of gyration, k= \(k=\sqrt { \frac { l }{ M } }\)

b. Theorem of parallel axes: This theorem is good for any shape. The moment of inertia of the body about any axis is equal to the sum of a moment of inertia of a.parallel axis passing through the center of mass and product of its mass of the body and square of the distance between the two parallel axes.

where I am the moment

c. Using parallel axes theorem, the moment of inertia about AB,

Answer 25.

a. Surface tension (a) is the property due to which the free surface of a liquid at rest behaves like an elastic stretched membrane tending to contract so as to occupy a minimum surface area.

Thus it is measured as the force acting per unit length of an imaginary line drawn on the liquid surface, the direction of force being perpendicular to this line and tangential to the liquid surface.

b. Consider a liquid drop of radius R and surface tension o. Let P be the excess pressure inside the drop. The work done by the force due to excess pressure is

c. On plowing, the gap between sand particles act as a capillary tube, so that groundwater reaches the surface easily due to capillary rise.

Answer 26.

b. Work was done in the adiabatic process: We have a small amount of work done when volume changes through at pressure P.

(volume changes from v_{1} to v_{2} diabolically)