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Physics for you|June ‘15 75

physics for you|june ‘15

1. A boy standing in an elevator observes a screw falls from the ceiling. The ceiling is 3 m above the floor.

(a) If the elevator is moving upward with a speed of 2.2 m s^–1, how long does it take for the screw to hit the floor? (b) How long is the screw in air if the elevator starts from rest when the screw falls, and moves upwards with a constant acceleration of a = 4 m s^–2?

2. An enemy fighter jet is flying at a constant height of 250 m with a velocity of 500 m s^–1. The fighter jet passes over an anti-aircraft gun that can fire at any time and in any direction with a speed of 100 m s^–1. Determine the time interval during which the fighter jet is in danger of being hit by the gun bullets.

3. A particle is to be projected from a point P so that it may strike the incline perpendicularly. Determine the required velocity of projection if it is horizontal initially.

4. A steel ball which can slide on a smooth rod of length L is attracted by an electromagnet. The force of attraction imparts an acceleration a = K/(L – x)², where K is constant and x is distance travelled.

If the ball is released from rest at x = 0, determine the velocity v with which it strikes the pole face.

5. The current velocity of a river grows in proportion to the distance from its bank and reaches the maximum value v₀ in the middle. Near the banks the velocity is zero. A boat is moving along the river in such a manner that it is always perpendicular to current and the speed of the boat in still water is u.

Find the distance through which the boat crossing the river will be carried away by the current if the width of river is c. Also trace the trajectory of boat.

6. A gas-filled spherical balloon is expanding.

The radius of sphere at time t is r. Find the radius when the rates of increase of the surface area and the radius are numerically equal.

7. A projectile is fired with velocity u from a gun adjusted for a maximum range. It passes through two points P and Q whose heights above the horizontal are h each. Show that the separation between the two is u

g u²−4gh.

8. A particle is moving in a circle of radius r in such a way that at any instant, the total acceleration makes an angle of 45° with radius. Initial speed of particle is u. Find the time taken to complete the first revolution.

By : Prof. Rajinder Singh Randhawa*

*Randhawa Institute of Physics, S.C.O. 208, First Fl., Sector-36D & S.C.O. 38, Second Fl., Sector-20C, Chandigarh, Ph. 09814527699

physics for you |june ‘15 77 SOLUTIONS

1. (a) Consider the elevator floor to be origin. It moves with a constant velocity. Equation for floor

y_f = v_ft = 2.2t ...(i) The screw falls with

acceleration due to gravity

2. The equation of trajectory of bullet is

y x gx For a given value of x, maximum y can be deter-mined from

The bullet can hit an area defined by

y ug

On substituting given values, we get

x² x

The equation of trajectory of particle is y h gx

= − 1 v 2

02 ...(ii)

The incline is a straight line, its equation is

y = xtanq ...(iii)

4. Acceleration of ball, a K

= L x

physics for you|june ‘15

It represents the equation of a parabola.0

When y c x cv

7. The trajectory of projectile is given by

y x gx

= tanq− u₂²( tan )+ ²q

2 1

Gun is adjusted for maximum range, i.e., q = 45°

\ y x gx= −

8. Since, tangential acceleration (a_t) = radial

acceleration (a_r) ( q = °45)

which gives T r

u e

= (1− ⁻^2p)

Physics for you|june ‘15

1. A particle in uniform circular motion can possess (a) radial acceleration only

(b) tangential acceleration only

(c) both radial and tangential acceleration (d) neither radial nor tangential acceleration 2. Which of the following physical quantities is not

dimensionless ? (a) Relative density (b) Relative velocity (c) Relative refractive index (d) Relative permittivity

3. The numerical ratio of displacement to the distance covered is always

(a) less than one (b) equal to one

4. A student unable to answer a question on Newton’s laws of motion attempts to pull himself up by tugging on his hair. He will not succeed because (a) the force exerted is small.

(b) the frictional force while gripping is small.

(d) the force applied is internal to the system.

5. If mass-energy equivalence is taken into account when water is cooled to form ice, the mass of water should

(a) increase

(b) remain unchanged (c) decrease

(d) first increase then decrease

6. Which one of the following waves does not involve oscillations of particles of a medium?

(a) Waves in a hanging spring (b) Ripples on a water surface (c) A light wave

(d) Ultrasonic waves

7. If a body is projected with an angle q to the horizontal, then

(a) its velocity is always perpendicular to its acceleration.

(b) its velocity becomes zero at its maximum height.

(d) the body just before hitting the ground, the direction of velocity coincides with the acceleration.

8. The internal energy of an ideal gas depends on which of the following factors?

(a) Pressure only (b) Volume only (c) Temperature only

(d) Pressure, volume and temperature

9. Bernoulli’s principle is not involved in the working/

explanation of

(a) movement of spinning ball (b) blades of a kitchen mixer (c) heart attack

(d) dynamic lift of an aeroplane

10. The temperature of the system decreases in the process of

(a) isothermal expansion (b) adiabatic expansion (c) isothermal compression (d) adiabatic compression

11. A wire is stretched under a force. If the wire suddenly snaps, the temperature of the wire, (a) remains the same

(b) decreases (c) increases

(d) first decreases then increases

12. For a constant volume gas thermometer, one should fill the gas at

(a) low temperature and low pressure (b) low temperature and high pressure (c) high temperature and low pressure (d) high temperature and high pressure

Physics for you|june ‘15 81 13. Which of the following forces is a contact force?

(a) Gravitational force (b) Electrostatic force (c) Magnetic force (d) Buoyant force

14. Which of the following characteristics does not change due to the damping of simple harmonic motion ?

(a) Angular frequency (b) Time period (c) Initial phase (d) Amplitude

15. A cricket bat is cut at the location of its centre of mass as shown. Then

(a) the two pieces will have the same mass.

(b) the bottom piece will have larger mass.

(d) mass of handle piece is double the mass of bottom piece.

16. Which of the following thermodynamic variables is an extensive variable ?

(a) Temperature (b) Pressure (c) Internal energy (d) Density

17. Angle between wave velocity and particle velocity of a longitudinal wave is

(a) 90° (b) 60° (c) 0° (d) 120°

18. If there were no gravity, which of the following will not be there for a fluid ?

(a) Viscosity (b) Surface tension (c) Pressure

(d) Archimedes’ upward thrust

19. A lead ball falling freely from a height strikes the ground, as a result its temperature rises. This is due to (a) friction of air

(b) conversion of chemical energy into heat (c) conversion of mass into heat

(d) conversion of mechanical energy into heat 20. Which of the following quantities is zero on an

average for the molecules of an ideal gas in equilibrium ? (a) Kinetic energy (b) Momentum

21. In a simple harmonic oscillator, at the mean position

(a) kinetic energy is minimum, potential energy is maximum.

(b) both kinetic and potential energies are maximum.

(d) both kinetic and potential energies are minimum.

22. In planetary motion, the angular momentum conservation leads to the law of

(a) orbits (b) areas

(d) conservation of linear momentum 23. Energy is not transferred by

(a) transverse progressive wave (b) longitudinal progressive wave (c) stationary wave

(d) electromagnetic wave

24. Which of the following is not an illustration of Newton’s third law ?

(a) Flight of a jet plane

(b) A cricket player lowers his hands while catching a cricket ball

25. Hydrostatic paradox states that the pressure exerted by a liquid

(a) depends on the shape of the containing vessel and independent of height of liquid column.

(b) depends on both shape of the containing vessel and height of liquid column.

(d) depends on height only and independent of the shape of the containing vessel.

soLuTioNs

1. (a) : A particle in uniform circular motion can possess radial acceleration only.

2. (b) : Relative velocity has the dimensions of velocity.

3. (c) : Since displacement is always less than or equal to distance covered, but never greater than distance covered. Hence the numerical ratio of displacement to the distance covered is always equal to or less than one.

4. (d) : According to Newton’s first law of motion, the state of rest or motion of body in a straight line with uniform velocity remains the same unless an external force is applied on the body. Internal forces are the forces which are exchanged by the particles in the system.

5. (c) : When water is cooled to form ice, its thermal energy decreases. By mass-energy equivalence, the mass of water should decrease.

6. (c) : A light wave is an electromagnetic wave.

It does not require a medium for propagation.

A man may imagine things that are false, but he can only understand things that are true, for if the things be false, the apprehension of them is

not understanding

-Sir Isaac Newton

Physics for you|june ‘15

7. (c) : In angular projection, the body at the highest point has velocity =ucosq in the horizontal direction which makes zero angle with the horizontal direction.

8. (c) : The internal energy of an ideal gas depends only on temperature.

9. (b) : Movement of spinning ball, heart attack and dynamic lift of an aeroplane, all are based on the Bernoulli’s principle.

10. (b) : In an adiabatic expansion the temperature of the system decreases while in an adiabatic compression it increases.

In an isothermal expansion or isothermal compression the temperature of the system remains constant.

11. (c) : The work done on the wire to produce a strain in it will be stored as energy which is converted into heat when the wire snaps suddenly. Due to it, the temperature of the wire increases.

12. (c)

13. (d) : Among the given forces buoyant force is a contact force whereas all others are non-contact forces.

14. (c)

15. (b): The centre of mass is closer to massive part of the body therefore the bottom piece of bat has larger mass.

16. (c) : Among the given thermodynamics variables internal energy is an extensive variable whereas all others are intensive variables.

17. (c) : In a longitudinal wave the particles of the medium oscillate along the direction of wave motion. Thus the angle between wave velocity and particle velocity is 0°.

18. (d) : For a fluid, Archimedes’ upward thrust will not be present if there were no gravity.

19. (d) 20. (b)

21. (c) : At the mean position, the kinetic energy is maximum and potential energy is minimum.

22. (b) : Angular momentum conservation leads to the law of areas.

23. (c) : Energy is not transferred by stationary wave but it is transferred by all others.

24. (b) : A cricket player lowers his hands while catching a cricket ball is an illustration of Newton’s second law, whereas all others are illustrations of Newton’s third law.

25. (d)

physics for you|June ‘15

Q1. How does cooking happen in a microwave oven?

– Abhishek Yadav (U.P.)

Ans. Microwave oven heats and cooks food by exposing it to electromagnetic radiation in the microwave spectrum. Passage of microwaves through food results in increased agitation of molecules. Microwave induces polarized molecules in the food to rotate and produce in a process known as dielectric heating. At microwave frequencies, the alternating electric field of the radiation interacts with the electric dipole moment of water molecules, making them vibrate faster. The absorption length of the microwave energy is long, that means not all energy falling on a chunk of cooking food gets absorbed while traversing through it. It also mean that the heating occurs all through the body of the food. That is the reason you do not get a crisp surface on the outside, as you would in normal cooking where the heat has to travel inwards from outside. When you cook a big chunk of raw food in a pan on open fire, the surface might become crisp, while the inside might remain relatively raw. Also remember that a microwave oven is an enclosure whose walls have excellent reflecting properties. Therefore, the fact that little microwave energy is absorbed upon initial traversal through the chunk of food does not mean the rest of the energy is lost, the reflective metallic walls of the oven bounce the microwaves back and forth to ensure repeated interaction with water contained in the food.

Q2. What causes a flag on a flagpole to flap even in a moderate breeze? – Anoop Kumar (Bihar)

Ans. Imagine that the plane of the flag is at an angle to the direction of the passing air so that the air pushes against one side of the flag. That push can simply straighten out the flag, making it extend in the direction of the airflow. Instead, the push can bend the flag. If the airspeed is above a certain critical value, this bending can become unstable and the flag will then flutter.

The fluttering has often been attributed to vortex formation by the flag. Indeed, whether the wind merely extends the flag or causes it to flutter, the free end of the flag sheds vortexes, that is, alternating on the left and right side of the flag, form and then move downstream. The vortexes are larger if the flag flutters, but they are a product of, not the cause of, the fluttering and they can be present even if the flag is not fluttering.

Q3. What causes water waves? How are they generated?

– Akshi Sharma (Delhi)

Ans. These two questions are not yet clearly answered.

However, a simple explanation is as follows. A breeze or some disturbance in the air or water creates ripples.

The ripples can then grow into larger waves as wind moves across them. In particular, the wind pushes on the windward side of a crest, comes over the crest, and then breaks up into vortexes, and so the pressure difference between the windward and leeward sides of the crest can push the crest downwind and also make it taller. In other words, the wind can feed energy into the crest. If the wind becomes stronger, the waves grow larger and their wavelengths also change.

Q4. Electric field for a point charge is proportional to 1/r² but electric field for a dipole is proportional to 1/r³. Why? – Anubhab Banerjee (W.B.)

Ans. Experimentally, electric field due to a point charge is given by E q

r E

= 1 ∝r

0 2 2

πε ; .

Now electric dipole is the distribution of some charges which give net charge on dipole zero and potential due to it, V p

r V

= 1 ∝r

0 2 2

πε ,

(For simplicity we take dipole as two oppositely charges of same magnitude separated by a very small distance.)

Also, E dV

= − dr

So electric field due to dipole, E

∝ 1r₃ Note : For infinitely line charge, E

∝ 1. So electric r field due to any charge system depends on its

distribution. 

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across

3. The ratio of the total absorbed radiation to the total incident radiation. (11)

5. The fraction of solar energy reflected from the earth back into space. (6) 11. Short form of quasi-stellar radio

source. (6)

13. Black body radiation that is predicted to be released by black holes, due to quantum effects near the event horizon. (7, 9)

16. A collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, like solids and some liquids. (6)

19. Carrier of strong nuclear force. (5) 20. A hypothetical set of multiple

possible universe which exist in parallel with each other. (10)

21. A unit of atmospheric pressure equivalent to 1000 dyne per cm². (8)

22. A branch of physics applied to technology that makes use of gas or pressurized air. (10)

23. A mechanism that converts rotational motion to linear motion and a torque to a linear force. (5)

24. CGS unit of magnetic field strength. (7)

25. The division between two regions of differing physical properties. (8)

26. The phenomenon that consists of a given system being driven by another vibrating system or by external forces to oscillate with greater amplitude at some preferential frequencies. (9)

1. DoWNSingle disturbance moving through a medium or fluid.

(4, 5)

2. The dark lines in the spectrum of sun. (10)

4. The temperature of steam over pure boiling water under 1 atm pressure. (5, 5)

6. A hypothetical type of nuclear reaction that would occur at or near room temperature. (4, 6)

7. A group of lines in the ultraviolet region in the spectrum of hydrogen. (5, 6)

8. The study of magnets and magnetism. (11) 9. Subatomic particle composed of three quarks. (6) 10. The lowest possible energy of molecular vibration.

(4, 5, 6)

12. The branch of mechanics that deals with matter and forces in equilibrium. (7)

14. A hypothetical tunnel through space time that connects widely distant regions thus providing a shortcut through space time. (8)

15. The melting point of ice under 1 atm pressure. (3, 5) 17. An electrical device that converts thermal energy into

electrical energy. (10)

18. The theory that nature contains no vacuums. (7) 20. A magnesium alloy used to enclose uranium fuel element

in certain types of nuclear reactors. (6)



Physics for you|june ‘15

In document Physics for You June 2015 (Page 68-80)