1. The resolving power of an electron microscope is higher than that of an optical microscope because the wavelength of electron is ---- than the wavelength of visible light.
2. In the Bohr model of the hydrogen atom, the ratio of the kinetic energy to the total energy of the electron in a quantum state n is _______.
3. Five point charges, each of value +q, are placed on five vertices of a regular hexagon of side L. The magnitude of the force on a point charge of value -q placed at the centre of the hexagon is _______ netwtons.
4. A ray of light undergoes deviation of 30° when incident on an equilateral prism of refractive index √2. The angle made by the ray inside the prism with the base of the prism is ______ .
5. A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with the track is
a. zero b. 45° c. 30° d. 60°
Source 1992 JEE
Sunday, October 11, 2009
IIT JEE Physics Final Revision Set 6
Two thin circular discs of mass 2 Kg and radius 10 cm each are joined by a rigid massless rod of length 20 cm. The axis of the rod is along the perpendicular to the planes of the disk through their centres. This object is kept on a truck in such a way that the axis of the object is horizontal and perpendicular to the direction of motion of the truck. Its friction with the floor of the truck is large enough so that the object can roll on the truck without slipping. Take x-axis as the direction of motion of the truck and z-axis as the vertically upwards direction. If the truck has an acceleration 9 m/s2, calculate:
1. the force of friction on each disk.
2. the magnitude and direction of the frictional torque acting on each disk about the centre of mass O of the object.
3. Express the torque in the vector form in terms of unit vectors i, j and k in x, y and z directions.
4. In the following column I lists some physical quantities and the column II gives approximate energy of them. Choose the appropriate value of energy from column II for each of the physical quantities in column I
Column I ------------- Column II
(i) Energy of thermal neutron---- (A) 0.025 eV
(ii) Energy of X-Ray ------------ (B) 0.5 eV
(iii) Binding energy per nucleon-- (C) 3 eV
(iv) Photoelectric threshold of a metal --- (D) 20 eV
------------------------------------------ (E) 10 keV
-------------------------------------------(F) 8 MeV
5. A band playing music at a frequency f is moving towards a wall at a speed Vb. A motorist is following the band with a speed Vm. If V is the speed of sound, obtain an expression for the beat frequency heard by the motorist.
Source JEE paper 1997
1. the force of friction on each disk.
2. the magnitude and direction of the frictional torque acting on each disk about the centre of mass O of the object.
3. Express the torque in the vector form in terms of unit vectors i, j and k in x, y and z directions.
4. In the following column I lists some physical quantities and the column II gives approximate energy of them. Choose the appropriate value of energy from column II for each of the physical quantities in column I
Column I ------------- Column II
(i) Energy of thermal neutron---- (A) 0.025 eV
(ii) Energy of X-Ray ------------ (B) 0.5 eV
(iii) Binding energy per nucleon-- (C) 3 eV
(iv) Photoelectric threshold of a metal --- (D) 20 eV
------------------------------------------ (E) 10 keV
-------------------------------------------(F) 8 MeV
5. A band playing music at a frequency f is moving towards a wall at a speed Vb. A motorist is following the band with a speed Vm. If V is the speed of sound, obtain an expression for the beat frequency heard by the motorist.
Source JEE paper 1997
IIT JEE Physics Final Revision Set 5
Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fasted photoelectrons emitted from sodium is 0.73 eV. The work function for sodium is 1.82 eV.
Find
1. the energy of the photons causing the photoelectric emission.
2. the quantum numbers of the two levels involved in the emission of these photons.
3. the change in the angular momentum of the electron in the hydrogen atom in the above transition.
4. the recoil speed of the emitting atom assuming it to be at rest before the transition. (Ionizatin potential of hydrogen is 13.6 eV.)
5.A plant observed by an astronomical refracting telescope having an objective of focal length 16 m and an eyepiece of focal length 2 cm.
a. The distance between the objective eye piece is 16.02 m.
b. The angular magnification of the planet is -800.
c. The image of the planet is inverted.
d. The objective is larger than the eyepiece.
Source; JEE 1992 paper
Find
1. the energy of the photons causing the photoelectric emission.
2. the quantum numbers of the two levels involved in the emission of these photons.
3. the change in the angular momentum of the electron in the hydrogen atom in the above transition.
4. the recoil speed of the emitting atom assuming it to be at rest before the transition. (Ionizatin potential of hydrogen is 13.6 eV.)
5.A plant observed by an astronomical refracting telescope having an objective of focal length 16 m and an eyepiece of focal length 2 cm.
a. The distance between the objective eye piece is 16.02 m.
b. The angular magnification of the planet is -800.
c. The image of the planet is inverted.
d. The objective is larger than the eyepiece.
Source; JEE 1992 paper
IIT JEE Physics Final Revision Set 4
A cart is moving along x direction with a velocity of 4 m/s. A person on the cart throws a stone with a velocity of 6 m/s relative to himself. In the frame of reference of the cart the stone is thrown in y-z plane making an angle of 30° with vertical z axis. At the highest point of its trajectory the stone hits an object of equal mass hung vertically from branch of a tree by means of a string of length L.A completely inelastic collision occurs in which the stone gets embedded in the object.
Determine :
1. The speed of the combined mass immediately after the collision with respect to an observer on the ground.
2. The length L of the string such that the tension in the string becomes zero when the string becomes horizontal during the subsequent motion of the combined mass.
Two blocks of mass m1 = 10 Kg and m2 = 5 Kg connected to each other by a massless inextensible string of length 0.3 m are placed along a diameter of turn table. The coefficient of friction between the table and m1 is 0.5 while there is no friction between m2 and the table. The table is rotating with an angular velocity of 10 rad/s about a vertical axis passing through its centre O. The masses are placed along the diameter of the table on either side of the centre O such that the mass m1 is at a distant of 0.124 m from O. The masses are observed to be at rest with respect to an observer on the turn table.
3. Calculate the frictional force on m1.
4. What should be the minimum angular speed of the turn tale so that the masses will slip from this position.
5. How should the masses be placed with the string remaining taut so that there is no frictional force acting on the mass m1.
Source: 1997 JEE paper
Determine :
1. The speed of the combined mass immediately after the collision with respect to an observer on the ground.
2. The length L of the string such that the tension in the string becomes zero when the string becomes horizontal during the subsequent motion of the combined mass.
Two blocks of mass m1 = 10 Kg and m2 = 5 Kg connected to each other by a massless inextensible string of length 0.3 m are placed along a diameter of turn table. The coefficient of friction between the table and m1 is 0.5 while there is no friction between m2 and the table. The table is rotating with an angular velocity of 10 rad/s about a vertical axis passing through its centre O. The masses are placed along the diameter of the table on either side of the centre O such that the mass m1 is at a distant of 0.124 m from O. The masses are observed to be at rest with respect to an observer on the turn table.
3. Calculate the frictional force on m1.
4. What should be the minimum angular speed of the turn tale so that the masses will slip from this position.
5. How should the masses be placed with the string remaining taut so that there is no frictional force acting on the mass m1.
Source: 1997 JEE paper
Saturday, September 5, 2009
IIT-JEE-Physics-Revision Questions - Set 3
1. A laser beam λ = 666 nm has a power of 3 mW. Find the pressure exerted on a surface by this beam if the cross sectional area is 3 nm². Assume perfect reflection as normal incidence.
2. A hydrogen-like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transitions between a group of levels. These levels have energies between -0.85 eV and -0.544 eV (including both these values). Find the atomic number of the atom.
Take hc = 1240 eV-nm, ground state energy of hydrogen atom = -13.6 eV.
3. The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state is
(a) 2.82 ms-1
(b)4.178 ms-1
(c)8.356 ms-1
(d)6.817 ms-1
4. An electron makes transition inside a hydrogen atom. The orbital angular momentum of the electron may change by
(a) h/2π (b) h/π (c)h/4π (d)h/3π
Multiple options are possible
5. Nuclei of radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N0 nuclei of the element. Calculate the number N of nuclei of A at time t.
2. A hydrogen-like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transitions between a group of levels. These levels have energies between -0.85 eV and -0.544 eV (including both these values). Find the atomic number of the atom.
Take hc = 1240 eV-nm, ground state energy of hydrogen atom = -13.6 eV.
3. The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state is
(a) 2.82 ms-1
(b)4.178 ms-1
(c)8.356 ms-1
(d)6.817 ms-1
4. An electron makes transition inside a hydrogen atom. The orbital angular momentum of the electron may change by
(a) h/2π (b) h/π (c)h/4π (d)h/3π
Multiple options are possible
5. Nuclei of radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N0 nuclei of the element. Calculate the number N of nuclei of A at time t.
Sunday, August 23, 2009
IIT - JEE- Physics - Revision Questions - Set 2 - Past JEE Questions
1. A uniform rigid rod of mass M and length L is standing vertically along the y-axis on a smooth horizontal surface, with its lower end at the origin (0,0). A slight disturbance at t = 0 causes the lower end to slip on the smooth surface along the positive x-axis, and the rod starts falling.
What is the path followed by the centre of mass of the rod during its fall?
2. A hemispherical bowl of radius R = 0.1 m is rotating about its own axis (which is vertical), with an angular velocity ω. A particle of mass 10-2 kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl.
Obtain the relation between h and ω. What is minimum value of ω needed, in order to have a non-zero value of h?
3. A cylindrical solid of mass 10-2 and cross-sectional area 10-4 m2 is moving parallel to its axis (the x-axis) with a uniform speed of 103 m/s in the positive direction. At t = 0, its front face passes the dust particles of uniform density 10-3 kg/m3. When a dust particle collides with the face of the cylinder, it sticks to its surface. Assuming that the dimensions of the cylinder remain practically unchanged, and that the dimensions of the cylinder remain practically unchanged, and that the dust sticks only to the front face of the cylinder, find the x-coordinate of the front of the cylinder at t = 150 s.
4. A circular ring of radius R with uniform positive charge density λ per unit length is located in the y-z plane with its centre at the origin O. A particle of mass m and positive charge q is projected from the point P(R√3,0,0) on the positive x-axis directly towards O, with an initial speed v. Find the smallest (non-zero) value of the speed v such that the particle does not return to P.
5. Two radio stations broadcast their programmes at the same amplitude A, and at slightly different frequencies ω1 and ω2 respectively, where ω2 - ω1 = 10³ Hz. A detector receives the signals from the two stations simulataneously. It can only detect signals of intensity ≥2A². Find the time interval between successive maxima of the intensity of the signal received by the detector.
Source (1993 JEE paper)
What is the path followed by the centre of mass of the rod during its fall?
2. A hemispherical bowl of radius R = 0.1 m is rotating about its own axis (which is vertical), with an angular velocity ω. A particle of mass 10-2 kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl.
Obtain the relation between h and ω. What is minimum value of ω needed, in order to have a non-zero value of h?
3. A cylindrical solid of mass 10-2 and cross-sectional area 10-4 m2 is moving parallel to its axis (the x-axis) with a uniform speed of 103 m/s in the positive direction. At t = 0, its front face passes the dust particles of uniform density 10-3 kg/m3. When a dust particle collides with the face of the cylinder, it sticks to its surface. Assuming that the dimensions of the cylinder remain practically unchanged, and that the dimensions of the cylinder remain practically unchanged, and that the dust sticks only to the front face of the cylinder, find the x-coordinate of the front of the cylinder at t = 150 s.
4. A circular ring of radius R with uniform positive charge density λ per unit length is located in the y-z plane with its centre at the origin O. A particle of mass m and positive charge q is projected from the point P(R√3,0,0) on the positive x-axis directly towards O, with an initial speed v. Find the smallest (non-zero) value of the speed v such that the particle does not return to P.
5. Two radio stations broadcast their programmes at the same amplitude A, and at slightly different frequencies ω1 and ω2 respectively, where ω2 - ω1 = 10³ Hz. A detector receives the signals from the two stations simulataneously. It can only detect signals of intensity ≥2A². Find the time interval between successive maxima of the intensity of the signal received by the detector.
Source (1993 JEE paper)
Saturday, August 22, 2009
Past IIT JEE Questions - Collection 1 (For JEE 2010)
1. A ball of density d is dropped on to a horizontal solid surface. It bounces elastically from the surface and returns to its original position in time t1. Next, the ball is released and it falls through the same height before striking the surface of a liquid of density dL. What is the expression for the time t2 the ball takes to come back to the position from which it was released in terms of d, t1 and dL. d is less than dL.
2. A straight segment of a circuit with length L is carrying a current I (in the positive direction of x). It is placed between two infinitely long conductors in which current I is flowing in opposite directions are placed perpendicular to it. What is the expression for th force acting on the circuit segment?
3. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fasted photoelectrons emitted from sodium is 0.73 eV. The work function for sodium is 1.82 eV. Find the energy of the photons causing the photoelectric emission.
4. A charge of Q is uniformly distributed over a spherical volume of radius R. What is the expression for the energy of the system?
5. Light is incident at an angle α on one planar end of a trasparent cylindrical rod of refractive index n. Determine the least value of n so that the light enteriing the rod does not emerge from the curved surface of the rod irrespective of the value of α.
(Source: 1992 JEE paper)
2. A straight segment of a circuit with length L is carrying a current I (in the positive direction of x). It is placed between two infinitely long conductors in which current I is flowing in opposite directions are placed perpendicular to it. What is the expression for th force acting on the circuit segment?
3. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The kinetic energy of the fasted photoelectrons emitted from sodium is 0.73 eV. The work function for sodium is 1.82 eV. Find the energy of the photons causing the photoelectric emission.
4. A charge of Q is uniformly distributed over a spherical volume of radius R. What is the expression for the energy of the system?
5. Light is incident at an angle α on one planar end of a trasparent cylindrical rod of refractive index n. Determine the least value of n so that the light enteriing the rod does not emerge from the curved surface of the rod irrespective of the value of α.
(Source: 1992 JEE paper)
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