Exam Details
Subject | Elementary Mechanics / Ocillations & Waves | |
Paper | ||
Exam / Course | Bachelor Degree Programme (Elective Course: Physics) | |
Department | School of Sciences (SOS) | |
Organization | indira gandhi national open university | |
Position | ||
Exam Date | June, 2016 | |
City, State | new delhi, |
Question Paper
1. Attempt any two parts:
A box of mass 40 kg is pulled on the floor by a light rope with a force 200 N. The rope makes an angle of 30° with the horizontal. Determine the acceleration of the box, if the coefficient of the kinetic friction between the floor and the box is 0·20. Draw the free body diagram. Identify the no-work forces from amongst the forces exerted on the box. Take g =10 ms^-2.
A circus artist falls straight on a safety net and rebounds vertically upwards at a speed of 3.0 ms^-l. Determine the maximum height reached by the artist with respect to the safety net. Take g =10 ms^-2.
How long must a force of 100 N be exerted to produce a change of 200 kg in the linear momentum?
State the law of conservation of energy. A block moves horizontally on a rough floor under a constant force of 10 N. The thermal energy of the block increases by 20 J after it travels a distance of 3.0 m. Calculate the increase in the thermal energy of the floor.
A constant torque of 20 Nm is exerted on a particle of mass 0·2 kg, initially at rest. The particle moves in a circle of radius 2.0 m. Determine the angular speed and angular momentum of the particle after 2.0 s. Is its angular momentum conserved?
2. Attempt anyone part
Derive the law of equal areas for central forces.
Write the expression for the centre of mass for a two-body system. Determine the centre of mass and relative coordinates of a system of two particles of masses 1·0 kg and 2·0 kg. The coordinates (in of the particles are and (3·0, 1·0), respectively. What is the reduced mass of the system?
Two atoms travelling towards each other with speeds of 100 and 20 respectively, undergo a head-on elastic collision. Calculate their speeds before and after the collision using the centre-of-mass frame of coordinates. It is given that their atomic masses are 10 amu and 20 amu, respectively.
OR
A ring and a disc, each of mass M and radius start from rest and roll without slipping down an inclined plane from the same height. Apply the principle of conservation of energy to determine which of them reaches the bottom of the incline first. Neglect friction.
A small ball of mass m is hanging from a string in a train. The train is moving with an acceleration a and the ball is at rest with respect to the train. For an observer in the train, calculate the angle that the string makes with the vertical. Analyse the motion in the non-inertial frame of reference.
OR
A bacteria of mass 5 x 10^-24 kg is rotated in a centrifuge at an angular speed of 4n x 10^3 rad It is situated at a distance of 10 cm from the axis of rotation. Calculate the effective value of g relative to the rotating frame of reference and the net centrifugal force on the bacteria.
4. Answer any three parts:
A train is approaching a railway station with a speed of 90 kmh^-1. The apparent frequency of the whistle heard by a person standing on the platform is 660 Hz.
Calculate the actual frequency of sound emitted by the train. Take the speed of sound in air as 330 ms^-1.
A string of mass per unit length 0·2 kg is stretched under a tension of 500 N. Calculate
the speed of transverse waves generated on the string, and
power of the travelling waves if amplitude is 1 cm. and wavelength is 0·5m.
The quality factor of a sonometer wire is 2 x 10^3. On plucking, the wire executes 240 vibrations per second. Calculate the time in which the amplitude will decrease to of its initial value.
A shock absorber acts like an elastic spring of force constant k. It compresses by 1 cm. when a mass m is placed on it. When this system is displaced from its equilibrium position, it begins to oscillate. Calculate the frequency of oscillations. Take g 10 ms^-2.
Two orthogonal harmonic oscillations having frequencies in the ratio of 2 1 are made to superpose. Determine the nature of the resultant oscillation, if their initial phases differ by n/2
5. Answer any two parts:
What is a compound pendulum? Obtain an expression for its time period. What do you understand by the equivalent length of a compound pendulum?
Define phase velocity and 'group velocity. The phase velocity of a wave propagating in a medium is given by
<img src='./qimages/11468-5b.jpg'>
where A is wavelength and a and b are constants. For what value of will group velocity be equal to phase velocity?
Transverse waves are incident on a boundary separating two media of different impedances. Write down the boundary conditions and obtain expressions for amplitude reflection and transmission coefficients.
A box of mass 40 kg is pulled on the floor by a light rope with a force 200 N. The rope makes an angle of 30° with the horizontal. Determine the acceleration of the box, if the coefficient of the kinetic friction between the floor and the box is 0·20. Draw the free body diagram. Identify the no-work forces from amongst the forces exerted on the box. Take g =10 ms^-2.
A circus artist falls straight on a safety net and rebounds vertically upwards at a speed of 3.0 ms^-l. Determine the maximum height reached by the artist with respect to the safety net. Take g =10 ms^-2.
How long must a force of 100 N be exerted to produce a change of 200 kg in the linear momentum?
State the law of conservation of energy. A block moves horizontally on a rough floor under a constant force of 10 N. The thermal energy of the block increases by 20 J after it travels a distance of 3.0 m. Calculate the increase in the thermal energy of the floor.
A constant torque of 20 Nm is exerted on a particle of mass 0·2 kg, initially at rest. The particle moves in a circle of radius 2.0 m. Determine the angular speed and angular momentum of the particle after 2.0 s. Is its angular momentum conserved?
2. Attempt anyone part
Derive the law of equal areas for central forces.
Write the expression for the centre of mass for a two-body system. Determine the centre of mass and relative coordinates of a system of two particles of masses 1·0 kg and 2·0 kg. The coordinates (in of the particles are and (3·0, 1·0), respectively. What is the reduced mass of the system?
Two atoms travelling towards each other with speeds of 100 and 20 respectively, undergo a head-on elastic collision. Calculate their speeds before and after the collision using the centre-of-mass frame of coordinates. It is given that their atomic masses are 10 amu and 20 amu, respectively.
OR
A ring and a disc, each of mass M and radius start from rest and roll without slipping down an inclined plane from the same height. Apply the principle of conservation of energy to determine which of them reaches the bottom of the incline first. Neglect friction.
A small ball of mass m is hanging from a string in a train. The train is moving with an acceleration a and the ball is at rest with respect to the train. For an observer in the train, calculate the angle that the string makes with the vertical. Analyse the motion in the non-inertial frame of reference.
OR
A bacteria of mass 5 x 10^-24 kg is rotated in a centrifuge at an angular speed of 4n x 10^3 rad It is situated at a distance of 10 cm from the axis of rotation. Calculate the effective value of g relative to the rotating frame of reference and the net centrifugal force on the bacteria.
4. Answer any three parts:
A train is approaching a railway station with a speed of 90 kmh^-1. The apparent frequency of the whistle heard by a person standing on the platform is 660 Hz.
Calculate the actual frequency of sound emitted by the train. Take the speed of sound in air as 330 ms^-1.
A string of mass per unit length 0·2 kg is stretched under a tension of 500 N. Calculate
the speed of transverse waves generated on the string, and
power of the travelling waves if amplitude is 1 cm. and wavelength is 0·5m.
The quality factor of a sonometer wire is 2 x 10^3. On plucking, the wire executes 240 vibrations per second. Calculate the time in which the amplitude will decrease to of its initial value.
A shock absorber acts like an elastic spring of force constant k. It compresses by 1 cm. when a mass m is placed on it. When this system is displaced from its equilibrium position, it begins to oscillate. Calculate the frequency of oscillations. Take g 10 ms^-2.
Two orthogonal harmonic oscillations having frequencies in the ratio of 2 1 are made to superpose. Determine the nature of the resultant oscillation, if their initial phases differ by n/2
5. Answer any two parts:
What is a compound pendulum? Obtain an expression for its time period. What do you understand by the equivalent length of a compound pendulum?
Define phase velocity and 'group velocity. The phase velocity of a wave propagating in a medium is given by
<img src='./qimages/11468-5b.jpg'>
where A is wavelength and a and b are constants. For what value of will group velocity be equal to phase velocity?
Transverse waves are incident on a boundary separating two media of different impedances. Write down the boundary conditions and obtain expressions for amplitude reflection and transmission coefficients.
Other Question Papers
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Subjects
- Astronomy and Astrophysics
- Communication Physics
- Electric & Magnetic Phenomena
- Electrical Circuits and Electronics
- Elementary Mechanics / Ocillations & Waves
- Mathematical Methods in Physics-I/ Mathematical Methods in Physics-II
- Mathematical Methods in Physics-III
- Modern Physics
- Optics
- Physics of Solids
- Thermodynamics & Statistical Mechanics