1. A circular disc of radius r/3 is removed from the outer-edge of a bigger circular disc of mass 9M and radius r. the moment of inertia of the remaining portion of the disc about the centre O of the disc perpendicular to the plane of the disc is
a. 4Mr²
b. (37/9)Mr²
c. (40/9)Mr²
d. 9Mr²
JEE 2005
Answer (a)
Solution
Mass of the disc removed
Total mass – M
Total area = π r²
Area of piece removed π (r/3) ²
Hence mass of the disc removed = M[π (r/3) ²]/( π r²) = M
Moment of inertia of removed about its own centre is = ½ (M)*(r/3) ²
Parallel axis theorem
Moment of inertia of a body about an axis parallel to its centre of mass is equal to
Moment of the body about the axis passing through its centre of mass plus Mr² (where M is the mass of body and r is the perpendicular distance between two axes.
According to the parallel axis theorem
Moment of inertia of the removed piece about an axis passing through the centre of the big disc = ½ (M)*(r/3) ² + M(2r/3) ²
=1/2(M) (r²/9) + M(4r²/9) = (½)(M) (r²/9 + 8r²/9) = (½)Mr²
Moment of inertia of bigger disc before cutting the piece
= ½ (9M)(r²)
Hence moment of inertia after removal of the piece
=( ½) (9M)(r²) - (½)Mr² = 4Mr²
Saturday, May 16, 2009
IIT JEE Level Revision Questions - 16. Sound waves
JEE Question
Sound waves of frequency 660 Hz fall normally on a perfectly reflecting wall. The shortest distance from the wall at which the air particles have the maximum amplitude of vibration is _____________ m. (JEE 1984 screening)
Answer 1/8
Revision Question 1
The equation of a travelling sound wave is y = 6.0 sin (600 t - 1.8 x) where y is measured in 10^-5 m. t in second and x in metre.
(a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave.
(b) Find the ratio of the velocity amplitude of the particles to the wave speed.
Source: HC Verma, Prob NO. 8)
Sound waves of frequency 660 Hz fall normally on a perfectly reflecting wall. The shortest distance from the wall at which the air particles have the maximum amplitude of vibration is _____________ m. (JEE 1984 screening)
Answer 1/8
Revision Question 1
The equation of a travelling sound wave is y = 6.0 sin (600 t - 1.8 x) where y is measured in 10^-5 m. t in second and x in metre.
(a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave.
(b) Find the ratio of the velocity amplitude of the particles to the wave speed.
Source: HC Verma, Prob NO. 8)
IIT JEE Level Revision Questions - 44. X-Rays
Past JEE Question
To produce charateristic X-rays using a Tungsten target in an X-ray generator, the accelerating voltage should be greater than ________ volts and the energy of the characteristic radiation is __________.
(The binding energy of the innermost electron in tungsten is 40 Kev).(JEE 1983 Screening)
Answer: 40 kV, 40 kV
Revision question 1
Find the maximum potential difference which may be applied across an X-ray tube with tungsten target without emitting any characteristic K or L X-ray.
The energy levels of the tungsten atom with an electron knocked out are as follows:
Cell---------------- Energy
containing---------- in
vacancy-------------keV
K -----------------69.5
L------------------11.3
M------------------ 2.3
(Reference: Problem No. 21 in HC Verma)
To produce charateristic X-rays using a Tungsten target in an X-ray generator, the accelerating voltage should be greater than ________ volts and the energy of the characteristic radiation is __________.
(The binding energy of the innermost electron in tungsten is 40 Kev).(JEE 1983 Screening)
Answer: 40 kV, 40 kV
Revision question 1
Find the maximum potential difference which may be applied across an X-ray tube with tungsten target without emitting any characteristic K or L X-ray.
The energy levels of the tungsten atom with an electron knocked out are as follows:
Cell---------------- Energy
containing---------- in
vacancy-------------keV
K -----------------69.5
L------------------11.3
M------------------ 2.3
(Reference: Problem No. 21 in HC Verma)
Tuesday, May 20, 2008
Monday, May 19, 2008
Saturday, May 17, 2008
Past JEE OQ - Wave Motion - Light Waves-1
Past JEE Objective Questions Wave Motion - Light Waves
Questions on light waves (Young’s double slit experiment)
1982
1. In Young’s double slit experiment the interference pattern is found to have an intensity ratio between bright and black fringes as 9. This implies that
a. the intensities due to the two slits are 5 units and 4 units respectively.
b. the intensities at the screen due to two slits are 4 units and 1 unit respectively.
c. the amplitude ratio is three.
d. the amplitude ratio is two.
1984
1. White light is used to illuminate the two slits in a Young’s double slit experiment. The separation between the slits is b and the screen is at a distance d (d>>b) from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths are
a. λ = b²/d
b. λ = 2b²/d
c. λ= b²/3d
d. λ= 2b²/3d
1986
1. In Young’s double slit experiment, the two slits act as coherent sources of equal amplitude A and of wavelength λ. In another experiment with the same set p the two slits are sources of equal amplitude A and wavelength λ, but are incoherent. The ratio of the intensity of light at the mid point of the screen in the first case to that in the second case is --------------.
1987
1. In a Young’s double slit experiment performed with a source of white light, only black and white fringes are observed.
1994
1. A beam of light of wavelength 600 nm from a distant source falls on a single slit of 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first dark fringes on either side of the central bright fringe is
a. 1.2 cm
b. 1.2 mm
c. 2.4 cm
d. 2.4 mm
1995
1. In an interference arrangement similar to Young’s double-slit experiment, the slits S1 and S2 are illuminated with coherent microwave sources, each of frequency 10^6 Hz. The sources are synchronized to have zero phase difference. The slits are separated by a distance of d = 150 m. The intensity of I(θ) is measured as a function of θ, where θ is defined as shown in the figure*. If I0 is the maximum intensity, the I(θ) for 0≤ θ ≤90° is given by
a. I(θ) = I0/2 for θ = 30°
b. I(θ) = I0/4 for θ = 90°
c. I(θ) = I0 for θ = 0°
d. I(θ) is constant for all values of θ
*(θ is the angle between the line joining the mid point of slits and its image on the screen and the line joining the image on the screen with mid pint of the slits)
1998
1. A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of the slit is
a. 0
b. π/2
c. π
d. 2 π
1999.
1. Yellow light is used in a single slit diffraction experiment with slit width of 0.6 mm. If yellow light is replaced by X-rays, then the observed pattern will reveal
a. that the central maximum is narrower.
b. more number of fringes
c. less number of fringes
d. no diffraction pattern
2000
1. In a doble slit experiment, instead of taking slits of equal widths, one slit is made twice as wide as the other. Then, in the interference pattern
a. the intensities of both the maxima and minima increase.
b. the intensity of the maxima increases and the minima has zero intensity.
c. the intensity of the maxima decreases and that of the minima increases.
d. the intensity of the maxima decreases and the minima has zero intensity.
2001
1. In a Young’s double slit experiment, 12 fringes are observed to be formed in a certain segment of the screen when light of wavelength 600 nm is used. If the wavelength is changed to 400 nm, number of fringes observed in the same segment of the screen is given by
a. 12
b. 18
c. 24
d. 30
2002
1. In an ideal double slit experiment, when a glass plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wavelength λ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass plate is
a. 2 λ
b. 2 λ/3
c. λ/3
d. λ
(optical path concept is to be used for this problem)
2004
1. In a Young’s double slit experiment, bichromatic light of wavelengths 400 nm and 560 nm are used. The distance between the slits is 0.1 mm and the distance between the slits and the screen is 1 m. The minimum distance between two minima is
a. 4 mm
b. 5.6 mm
c. 14 mm
d. 28 mm
2005
1. In a Young’s double slit experiment an electron beam is used to obtain interference pattern. If the speed of electrons decreased then
a. no interference pattern is observed.
b. distance between two consecutive fringes decreases
c. distance between two consecutive fringes increases.
d. distance between two consecutive fringes remains the same.
2. In a Young’s double slit experiment, the angular position θ of a bright fringe having intensity one fourth of the maximum intensity is given by
a. sin-1 (λ/4d)
b sin-1(λ/3d)
c. sin-1(λ/2d)
d. sin-1(λ/d)
(θ is the angle between the line joining the mid point of slits and its image on the screen and the line joining the image on the screen with mid pint of the slits)
Questions on light waves (Young’s double slit experiment)
1982
1. In Young’s double slit experiment the interference pattern is found to have an intensity ratio between bright and black fringes as 9. This implies that
a. the intensities due to the two slits are 5 units and 4 units respectively.
b. the intensities at the screen due to two slits are 4 units and 1 unit respectively.
c. the amplitude ratio is three.
d. the amplitude ratio is two.
1984
1. White light is used to illuminate the two slits in a Young’s double slit experiment. The separation between the slits is b and the screen is at a distance d (d>>b) from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths are
a. λ = b²/d
b. λ = 2b²/d
c. λ= b²/3d
d. λ= 2b²/3d
1986
1. In Young’s double slit experiment, the two slits act as coherent sources of equal amplitude A and of wavelength λ. In another experiment with the same set p the two slits are sources of equal amplitude A and wavelength λ, but are incoherent. The ratio of the intensity of light at the mid point of the screen in the first case to that in the second case is --------------.
1987
1. In a Young’s double slit experiment performed with a source of white light, only black and white fringes are observed.
1994
1. A beam of light of wavelength 600 nm from a distant source falls on a single slit of 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first dark fringes on either side of the central bright fringe is
a. 1.2 cm
b. 1.2 mm
c. 2.4 cm
d. 2.4 mm
1995
1. In an interference arrangement similar to Young’s double-slit experiment, the slits S1 and S2 are illuminated with coherent microwave sources, each of frequency 10^6 Hz. The sources are synchronized to have zero phase difference. The slits are separated by a distance of d = 150 m. The intensity of I(θ) is measured as a function of θ, where θ is defined as shown in the figure*. If I0 is the maximum intensity, the I(θ) for 0≤ θ ≤90° is given by
a. I(θ) = I0/2 for θ = 30°
b. I(θ) = I0/4 for θ = 90°
c. I(θ) = I0 for θ = 0°
d. I(θ) is constant for all values of θ
*(θ is the angle between the line joining the mid point of slits and its image on the screen and the line joining the image on the screen with mid pint of the slits)
1998
1. A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of the slit is
a. 0
b. π/2
c. π
d. 2 π
1999.
1. Yellow light is used in a single slit diffraction experiment with slit width of 0.6 mm. If yellow light is replaced by X-rays, then the observed pattern will reveal
a. that the central maximum is narrower.
b. more number of fringes
c. less number of fringes
d. no diffraction pattern
2000
1. In a doble slit experiment, instead of taking slits of equal widths, one slit is made twice as wide as the other. Then, in the interference pattern
a. the intensities of both the maxima and minima increase.
b. the intensity of the maxima increases and the minima has zero intensity.
c. the intensity of the maxima decreases and that of the minima increases.
d. the intensity of the maxima decreases and the minima has zero intensity.
2001
1. In a Young’s double slit experiment, 12 fringes are observed to be formed in a certain segment of the screen when light of wavelength 600 nm is used. If the wavelength is changed to 400 nm, number of fringes observed in the same segment of the screen is given by
a. 12
b. 18
c. 24
d. 30
2002
1. In an ideal double slit experiment, when a glass plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wavelength λ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass plate is
a. 2 λ
b. 2 λ/3
c. λ/3
d. λ
(optical path concept is to be used for this problem)
2004
1. In a Young’s double slit experiment, bichromatic light of wavelengths 400 nm and 560 nm are used. The distance between the slits is 0.1 mm and the distance between the slits and the screen is 1 m. The minimum distance between two minima is
a. 4 mm
b. 5.6 mm
c. 14 mm
d. 28 mm
2005
1. In a Young’s double slit experiment an electron beam is used to obtain interference pattern. If the speed of electrons decreased then
a. no interference pattern is observed.
b. distance between two consecutive fringes decreases
c. distance between two consecutive fringes increases.
d. distance between two consecutive fringes remains the same.
2. In a Young’s double slit experiment, the angular position θ of a bright fringe having intensity one fourth of the maximum intensity is given by
a. sin-1 (λ/4d)
b sin-1(λ/3d)
c. sin-1(λ/2d)
d. sin-1(λ/d)
(θ is the angle between the line joining the mid point of slits and its image on the screen and the line joining the image on the screen with mid pint of the slits)
Thursday, May 15, 2008
Questions paper files - Book 1
Resolution of forces
http://www.emanuelschool.org.uk/physics/alevel/aprobs/Mechanics/Resolution%20Of%20Forces.pdf
Simple harmonic motion
http://www.emanuelschool.org.uk/physics/alevel/aprobs/Mechanics/A2%20SHM.pdf
Waves
http://www.emanuelschool.org.uk/physics/alevel/aprobs/Mechanics/A2%20Waves.pdf
Gravitational force
http://www.emanuelschool.org.uk/physics/alevel/aprobs/A2gravity/Gravitational%20force.pdf
Orbital motion
http://www.emanuelschool.org.uk/physics/alevel/aprobs/A2gravity/Orbital%20motion.pdf
Gravitational field
http://www.emanuelschool.org.uk/physics/alevel/aprobs/A2gravity/Gravitational%20fields.pdf
http://www.emanuelschool.org.uk/physics/alevel/aprobs/Mechanics/Resolution%20Of%20Forces.pdf
Simple harmonic motion
http://www.emanuelschool.org.uk/physics/alevel/aprobs/Mechanics/A2%20SHM.pdf
Waves
http://www.emanuelschool.org.uk/physics/alevel/aprobs/Mechanics/A2%20Waves.pdf
Gravitational force
http://www.emanuelschool.org.uk/physics/alevel/aprobs/A2gravity/Gravitational%20force.pdf
Orbital motion
http://www.emanuelschool.org.uk/physics/alevel/aprobs/A2gravity/Orbital%20motion.pdf
Gravitational field
http://www.emanuelschool.org.uk/physics/alevel/aprobs/A2gravity/Gravitational%20fields.pdf
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