Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure.
The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m2 to stop the motion is
Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities +σ, -σ and +σ respectively. The potential of shell B is
An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, rα respectively in a uniform magnetic field B. The relation between re, rp, rα is :
The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:
The reading of the ammeter for a silicon diode in the given circuit is:
An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let λn, λg be the de Broglie wavelength of the electron in the nth state and the ground state respectively. Let Λn be the wavelength of the emitted photon in the transition from the nth state to the ground state. For large n, (A, B are constants)
The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 µm. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance ? (i.e. distance between the centres of each slit.)
In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be:
If fm is the modulation frequency in FM, the modulation index is proportional to
What should be the minimum length of the antenna capable of emitting audio signal of wavelength λ?
If the band width is 1.6 x 1012 Hz, how many communication channels can be obtained with 16 KHz band width radio signal?
An insulator used in a transmission line has dielectric constant equal to 0.25. What is the velocity factor of the transmission line?
A strip of copper and another germanium are cooled from room temperature to 80 K. The resistance of
If N0 is the original mass of the substance of half-life period t1/2 = 5 years, then the amount of substance left after 15 years is
If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is
The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (hc = 1240 eV.nm)
Energy required for the electron excitation in Li++ from the first to the third Bohr orbit is
If a source of power 4 kW produces 1020 photons/second, the radiation belongs to a part of the spectrum called
A charged oil drop is suspended in a uniform field of 3×104 v/m so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge = 9.9×10-15 kg and g = 10 m/s2)
Diameter of a plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is 2 × 108 m/s, the focal length of the lens is:
Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of Polaroid through 30° makes the two beams appear equally bright. If the initial intensities of the two beams are IA and IB respectively, then IA/IB equals:
A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is
The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in young’s double-slit experiment is
Let the x - z plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has refractive index of √2 and medium 2 with z < 0 has a refractive index of √3. A ray of light in medium 1 given by the vector A = 6√3i + 8√3j - 10k in incident on the plane of separation. The angle of refraction in medium 2 is
An electromagnetic wave of frequency v = 3.0 MHz passes from vacuum into a dielectric medium with permittivity ∈ = 4.0. Then
A boat is moving due east in a region where the earth's magnetic field is 5.0 × 10-5 NA-1m-1 due north and horizontal. The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50 ms-1, the magnitude of the induced emf is
A resistor 'R' and 2μF capacitor in series is connected through a switch to 20 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5s after the switch has been closed. (log102.5 = 0.4)
If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter a
If an electron and a proton having same momenta enter perpendicular to a magnetic field, then
The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its
A 3 volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current I, in the circuit will be
The current voltage relation of diode is given by I = (e1000V/T - 1) mA, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring ± 0.01 V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA?
Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t1 is the time taken for the energy stored in the capacitor to reduce to half its initial value and t2 is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio t1/t2 will be
A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then Q/q equals
If a charge q is placed at the centre of the line joining two equal charges Q such that the system is in equilibrium then the value of q is
On moving a charge of 20 coulombs by 2 cm, 2 J of work is done, then the potential difference between the points is
If θi is the inversion temperature, θn is the neutral temperature, θc is the temperature of the cold junction, then
Even Carnot engine cannot give 100% efficiency because we cannot
Three rods of Copper, Brass and Steel are welded together to from a Y-shaped structure. Area of cross-section of each rod = 4 cm2. End of copper rod is maintained at 100°C where as ends of brass and steel are kept at 0°C.
Lengths of the copper, brass and steel rods are 46, 13 and 12 cm respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is:
Heat given to a body which raises its temperature by 1°C is
Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively. The ratio of the energy radiated per second by the first sphere to that by the second is
A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V, the efficiency of the engine is
1 mole of a gas with γ = 7/5 is mixed with 1 mole of a gas with γ = 5/3, then the value of γ for the resulting mixture is