Rutherford performed the gold foil experiment that provided a new insight into structure of an atom. Their findings were not recognised by the scientific community of that time. |
Still this did not deter him from making further path breaking discoveries. |
(i) What kind of person was Rutherford? |
(ii) What was the conclusion of the gold foil experiment? |
(i) A parallel beam of light approaches a plane surface separating two media. If medium 'one' is optically denser and medium 'two' is optically rarer, using Huygen's principle, explain and show how a refracted wavefront is constructed? |
(ii) When a light wave travels from a rarer to a denser medium, the speed decreases. Does it imply reduction in its energy? Explain. |
Four identical cells, each of emf 8 V and internal resistance \[2.5\,\Omega ,\] are connected in series and charged by a 100 V DC supply, using a \[24\,\Omega \] resistor in series. |
Calculate the following |
(i) charging current in the circuit |
(ii) potential difference across the cells during recharging. |
Vishal on entering his apartment, switched ON the tubelight, but it did not work. So, he called the electrician. |
The electrician inspected the tubelight and suggested a replacement of the choke. |
On replacing the choke, Vishal found the tubelight working. |
(i) Identify the values of Vishal. |
(ii) What is the function of a choke in AC circuit? |
(iii) What is the effective resistance of a L-R circuit? |
A solenoid has a core of a material with relative permeability 400. The windings of the solenoid are insulated from the core and carry a current of 2A. If the number of turns is 1000 per metre, calculate |
(i) H (ii) B (iii) Magnetising current \[{{I}_{m}}.\] |
Where symbols have their usual meanings. |
An electric dipole of dipole moment p is placed in a uniform electric field E. Write the expression for the torque \[\tau \] experienced by the dipole. Show diagrammatically the orientation of the dipole in the field for which the torque is half of the maximum value. |
Or |
Two insulated charged copper spheres A and B have identical sizes and charge \[6.5\times {{10}^{-7}}\] C on each, and their centres are separated by distance of 50 cm. |
A third sphere C of same size but uncharged is brought in contact with first, then brought in contact with the second and finally removed from both, find the new force of interaction, between spheres A and B. |
Ram and Shyam went to a hill station in their summer vacation. During the outing, Shyam was shivering with cold. Ram put a blanket on him and ignited fire near by Shyam. After sometime, Shyam became normal. |
(i) What values did Ram show? |
(ii) What type of electromagnetic waves from the fire helped Shyam to become normal? |
(i) Write the truth table for the following circuit. Name the equivalent gate that this circuit represents. |
(ii) Two identical amplifiers are connected one after the other in series (cascaded). The first amplifier has a voltage gain of 20. If the input signal is 0.01 V then calculate the output of AC signal. |
If the nucleons of a nucleus are separated far apart from each other, the sum of masses of all these nucleons is larger than the mass of the nucleus. Where does this mass difference come from? Calculate the energy released, if \[{}^{238}U\] nucleus emits an \[\alpha \,\,\text{-}\,\text{particle}.\] |
Given, atomic mass of \[{}^{238}U=\text{ }238.05084\] amu atomic mass of \[{}^{234}Th=\text{ }234.04363\] amu atomic mass of \[\alpha -particle=4.00260\] amu and 1 amu\[=931\text{ }MeV/{{c}^{2}}\] |
Figure shows two identical capacitors \[{{C}_{1}}\] and \[{{C}_{2}},\] each of \[2\mu F\] capacitance, connected to a battery of 5 V. Initially switch S is closed. |
After sometime, S is left open and dielectric slabs of dielectric constant K = 5 are used and inserted to fill completely the space between the plates of the two capacitors. How will the (i) charge and (ii) potential difference between the plates of the capacitors be affected after the slabs are inserted? |
(i) In a Young's double slit experiment, the two slits are kept 2 mm apart and the screen is positioned 140 cm away from the plane of the slits. The slits are illuminated with light of wavelength 600 nm. Find the distance of the third bright fringe, from the central maximum, in the interference pattern obtained on the screen. |
(ii) If the wavelength of the incident light were changed to 480 nm, then find out the shift in the position of third bright fringe from the central maximum. |
Or |
A convex lens of focal length 10 cm is placed coaxially 5 cm away from a concave lens of focal length 10 cm. If an object is placed 30 cm in front of the convex lens, find the position of the final image formed by the combined system. |
During the replacing of the fuse wire in the power supply box of his house, Anil was got shocked and collapsed on the floor. After seeing this Anil's friend Ajay ran to him and with the help of a wooden stick switched OFF the main supply. |
(i) Write down the qualifies shown by Ajay. |
(ii) What is the voltage and frequency of AC supply in India? |
(iii) Write down advantages of AC over DC. |
A compound microscope uses an objective lens of focal length 4cm and eyepiece lens of focal length 10cm. An object is placed at 6cm from the objective lens. |
Calculate the magnifying power of the compound microscope. If final image is formed at the least distance of distinct vision. Also, calculate the length of microscope. |
(i) Using de-Broglie's hypothesis, explain with the help of a suitable diagram, Bohr's second postulate of quantisation of energy levels in a hydrogen atom. |
(ii) The ground state energy of hydrogen atom is \[-13.6\text{ }eV\] What are the kinetic and potential energies of the electron in this state? |
Ramesh and his younger brother Raju went to a shopping mall whose doors were automatic with self close and open. Raju asked Ramesh that, "How these doors automatically open and close without even a single touch?". |
Ramesh was a graduate, but he did not know the exact reason behind this. Ramesh asked the same from his friend Rakesh who was junior to him. Rakesh explained the whole phenomenon easily to Ramesh and told that this whole phenomenon is based on photoelectric effect given by the great scientist Einstein. |
(i) After reading the passage, what are your opinions about the education of Ramesh and describe about all three characters Ramesh, Rakesh and Raju in your words. |
(ii) State the laws of photoelectric effect. |
(iii) Write photoelectric equation given by Einstein and define photoelectric current. |
What is modulation index? Its value is kept always less than one in practice, explain its reason. |
A carrier wave of frequency 1.75 MHz, an amplitude 60V is modulated by a sinusoidal wave of frequency 12kHz producing 60% amplitude modulation. Find out the amplitude of the amplitude modulation wave. |
Draw the transfer characteristics of a common emitter n-p-n transistor. Point out the region in which the transistor operates as an amplifier. |
Define the following terms used in transistor amplifiers. |
(i) Input resistance |
(ii) Output resistance |
(iii) Current amplification factor |
Why is it that while using a moving coil galvanometer as a voltmeter a high resistance in series is required whereas in ammeter a shunt is used? |
A straight horizontal conducting rod of length 0.45 m and mass 60g is suspended by two vertical wires at its ends. A current of 5 A is set up in the rod through the wires. |
(i) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero? |
(ii) What will be the total tension in the wires, if the direction of current is reversed keeping the magnetic field same as before? (Ignore the mass of the wires) \[(g=9.8\,m{{s}^{-2}}).\] |
(i) What is the value of\[\varepsilon ?\] |
(ii) What purpose does the high resistance of \[600\,k\,\Omega \] have? |
(iii) Is the balance point affected by this high resistance? |
(iv) Is the balance point affected by the internal resistance of the driver cell? |
(v) Would the method work in the above situation, if the driver cell of the potentiometer had an emf of 1.0 V instead of 2.0 V? |
(vi) Would the circuit work well for determining extremely small emf, say of the order of a few mV (such as the typical emf of a thermocouple)? If not, how will you modify the circuit? |
Or |
(i) Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by |
\[({{E}_{2}}-{{E}_{1}})\cdot \hat{n}=\frac{S}{{{\varepsilon }_{0}}}\] |
where, \[\hat{n}\] is a unit vector normal to the surface at a. point and \[\sigma \] is the surface charge density at the point. (The direction of \[\hat{n}\] is from side 1 to side 2). Hence, show that just outside a conductor, the electric field is \[\sigma \hat{n}/{{\varepsilon }_{0}}.\] |
(ii) Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another. |
(i) What is the focal length of a convex lens of focal length 30 cm in contact with a concave lens of focal length 20 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses. |
(ii) At what angle should a ray of light be incident on the face of a prism of refracting angle \[60{}^\circ ,\] so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524. |
Or |
(a) Define the power of a lens. |
(b) What is the SI unit of a power? |
(c) Find the position of the image formed by the lens combination given in the following figure. |
(i) Explain the meaning of the term mutual inductance. Consider two concentric circular coils, one of radius \[{{r}_{1}}\] and the other of radius \[{{r}_{2}}\,\,({{r}_{1}}<{{r}_{2}})\] placed co-axially with centres coinciding with each other. Obtain the expression for the mutual inductance of the arrangement. |
(ii) A rectangular coil of area A, having number of turns N is rotated at \['f'\] revolutions per second in a uniform magnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is \[2\pi fNBA.\] |
Or |
Define mutual inductance of a pair of coils and write on which factors does it depends. |
(i) Magnetic flux \[(\phi )\] through the loop with time (t) |
(ii) Induced emf (e) in the loop with time (t) |
(iii) Induced current in the loop if it has resistance of \[0.1\,\Omega .\] |
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