Most Important Numerical Problems for CBSE 2018-19 by Dr. Mukesh Shrimali

Q.1 Consider two hollow concentric sphere S₁ and S₂ enclosing charges 2Q and 4Q respectively. Find out ratio of flux coming out from it. (Radius of S₁ is less than S₂).

Q.2 The ground state energy of hydrogen atom is – 13.6 eV. What is the kinetic and potential energies of the electron in this state?

Q.3Calculate the wave number of the line when electron make transition from n=2 to n=1 orbit in H atom ( RH = 1.097 × 10⁷ SI )

Q.4 Calculate the energy of photon of wavelength 6 × 10^-8m. How much excitation potential is needed for this excitation ?

Q.5 A 12.1 eV beam is used to bombard gaseous hydrogen at room temperature. What series of wavelength will be emitted?

Q.6 For the network shown, find the potential difference between A and B and between B and C in steady state.

Q.7 A network of four 10 F capacitors is connected to a 500 V supply as shown in Fig. Determine

(a) the equivalent capacitance of the network,
(b) the charge on each capacitor.

Q.8 The electric field at a point due to a point charge is 20 NC^–1 and the electric potential at that point is 10 JC^–1. Calculate the distance of the point from the charge and the magnitude of the charge

Q.9 A wire of resistance 10 ohm is drawn out so that its length is thrice its original length. Calculate its new resistance (resistivity and density of the material remain uncharged).

Q.10 The three stable isotopes of Neon have respective abundances of 90.51% ,0.27% and 9.22%. The atomic masses of the three isotopes are 19.99, 20.99 and 21.99 amu Obtain average atomic mass of neon.

Q.11A radioactive isotope has a half-life of 5 years. After how much time its activity reduced to 3.125% of its original

Q.12Double-convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length of the lens is to be 20 cm?

Q.13A compound microscope uses an objective lens of focal length 4 cm and eye piece lens of focal length 10 cm. An object is placed at 6 cm from the objective lens. Calculate the magnification power of the compound microscope. Also calculate length of the microscope.

Q.14Calculate the wavelength of radiation emitted when electron in a hydrogen atom jumps from n=∞ to n=1

Q.15 A screen is placed at a distance of 100 cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of the lens separated by 20 cm. Calculate the focal length of the lens used.

Q.16 A converging lens is kept coaxially in contact with a diverging lens both the lenses being of equal focal length. What is the focal length of the combination ?

Q.17Light passes through two polaroid’s P₁ and P₂ with its axis making an angle θ with the pass axis of P₁. For what value of θ intensity of light will be zero. A third polaroid is placed between P₁ and P₂ with its axis making an angle β with pass axis of P₁. Find the value of β for which the intensity of emerging light from P₂ is I₀/8, where I₀ is the intensity of light on the polaroid P₁.

Q.18A beam of light consisting of two wavelength 800nm and 600nm is used to obtain the interference fringes in a young’s double slit experiment on a screen placed 1.4 m away. If the two slits are separated by 0.28 mm, calculate the least distance from the central bright maxima where the bright fringes of the two wavelengths coincides.

Q.19 Two moving coil meters M1 and M2 have the following particulars
R₁ = 10Ω N₁ = 30 A₁ = 3.6×10^-3 m² B₁ = 0.25 T
R₂ = 14Ω N₁ = 42 A₂ = 1.8×10^-3 m² B₁ = 0.50 T
Determine the ratio of Current Sensitivity and Voltage Sensitivity.

Q.20A pair of adjacent coil has a mutual inductance of 1.5 H If the current in one coil changes from 0 to 20A in 0.5 Sec, what is the change of flux linkage with the other coil ?

Q.21In a meter bridge with R and S in the gaps, the null point is found at 40 cm from A. If resistance of 12 ohm is connected in parallel with S , the null point occur at 50 cm from A. Determine the values of R and S.

Q.22Fig. shows a 2.0 V potentiometer used for the determination of internal resistance of a 1.5 V cell. The balance point of the cell in open circuit is 76.3 cm. When a resistor of 9.5Ω is used in the external circuit of the cell, the balance point shifts to 64.8 cm. length of the potentiometer wire. Determine the internal resistance of the cell.

Q.23The energy level diagram of an element is given below. Identify, by doing necessary calculations, which transition corresponds to the emission of a spectral line of wavelength 102.7 nm.

Q.24 Find voltage gain and power gain in a transistor amplifier in a common emitter when current gain is 66 and the input and output resistances are 0.5 k ohm and 59 k ohm

Q.25 A semiconductor has equal electron hole concentration 6 × 10⁸. On doping with certain impurity, electron concentration increases to 9 × 10¹² / m³
(i) Identify the new semiconductor obtained after doping
(ii) Calculate the New Hole concentration
(iii) How does the energy gap vary with doping.

Q.26 A transmitting antenna at the top of a tower has a height of 36 m and the height of the receiving antenna is 49 m . What is the maximum distance between them for satisfactory communication in the line of sight

Q.27 An oscillating LC circuit consisting of a 1.0nF capacitor and a 3 mH coil has a maximum voltage of 3 V.
(a) What is the maximum charge on the capacitor,
(b) The maximum current through the circuit
(c) The maximum energy stored in the magnetic field of the coil.

Q.28The work function of the following metals is given
Na = 2.75eV, K = 2.30eV, Mo = 4.17eV Ni= 5.15eV
Which of these metals will not show a photoelectric emission for 3300 A⁰

Q.29 X ray of wavelength λ fall on a photosensitive surface, emitting electrons prove that the de Broglie wavelength of electron emitted will be (λh/2mc)^1/2

Q.30 Estimate the angular separation between first order maximum and third minimum of the diffraction pattern due to a single slit of width 1mm when light of wavelength 600nm is incident normal on it.

Q.31 A circuit containing a 80mH inductor, and a 250 micro F capacitor in series is connected to a 240V,100 rad/sec supply .obtain rms value of current and total average power consumed by the circuit.

Q.32 A point source of monochromatic light is kept at the center of the bottom of a cylinder of radius of 15 cm. which contain water to a height of 7.0cm. calculate the area of water through which light emerge in air.

Q.33 Two spherical conductor of radius R₁ and R₂ are charged. If they are connected by a conducting wire find the ratio of the surface charge density.

Q.34 In the circuit diagram given in Fig. the cells E₁ and E₂ have emf’s 4V and 8V and internal resistances 0.5 ohm and 10 ohm respectively. Calculate the current in each resistance.

Q.35 Estimate distance of closest approach to the nucleus (Z = 80 ) if 7.7 MeV alpha particle before it come to rest.

Q.36A straight horizontal conducting rod of length 0.45 m and mass 60g is suspended by two vertical wires at its end. Current of 5A is setup in the rod through the wires. Find the magnitude and direction of magnetic field which should be set up in order that tension in the wire is zero.

Q.37 Find how de Broglie wavelength associated with the electron orbiting in the ground state would change when it jump in to the first excited state. Given R₀= 0.53 Angstrom E₀= -13.6 eV

Q.38 Find Magnification of telescope of objective lens of focal length 15 m and eye piece of 1.0 cm.If this telescope is used to view the moon what is the diameter of the image of the moon formed by the objective lens ?The diameter of the moon is 3.48× 10⁶ m and radius of lunar orbit is 3.8 × 10⁸m

Q.39 Two metallic spheres A and B having charges +4Q and -10Q are kept a certain distance apart. A third identical uncharged sphere C is first placed in contact with A and then with sphere B. Spheres A and B are then brought in contact then separated. Find the charges on the sphere A and B.

Q.40 Two Charges of magnitude -2Q and +Q are located at points (a, 0) and (4a, 0) . What is electric flux due to these charges through a sphere of radius 3a with its center at the origin ?

Q.41 A 12pF capacitor is connected to a 50V battery. How much electrostatics energy is stored in the capacitor? If another capacitor of 6pF is connected across the combination find the charge stored and potential differences across each capacitor.

Q.42 A resistance of R draws current from a potentiometer. The potentiometer wire AB has a total resistance of R₀. A voltage V is supplied to the potentiometer. Derive an expression for the voltage across R when the sliding contact is in the middle of potentiometer wire.

Q.43 Two cells of emf E₁ and E₂ and internal resistance r₁ and r₂ are connected in parallel. Obtain the expression for the emf and internal resistance of single equivalent cell that can be replaced this combination

Q.44 A proton and an α – particle move perpendicular to a magnet field. Find the ratio of radii of circular paths described by them when both have
(i) equal velocities
(ii) equal kinetic energy

Q.45 You are given three lenses L₁ ,L_2/ and L₃ each of local 20cm. An object is kept at 40 cm in front of L₁. as shown. The final real image is formed at the formed at focus of L₃. Find separation between L₁,L₂, and L₃.

Q.46A convex lens made up of glass of refractive index 1,5 is dipped, in turn in medium of refractive index 1.65 (ii) medium of refractive index 1.33
(a) Will it behave as a converging or a diverging lens in the two cases ?
(b) How will its focal length changes in the two media ?

Q.47 In young double slit experiment using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path difference is λ ,is K unit. Find out the intensity of light where path difference is λ/3

Q.48 The wavelength of light from the spectral emission of sodium is 589nm. Find the KE of the electron for which it would have the same de- Broglie wavelength