An electric dipole consists of charges \[\pm 2.0\times {{10}^{-8}}C\]separated by a distance of \[2.0\times {{10}^{-3}}m\]. It is placed near a long line charge of linear charge density \[4.0\times {{10}^{-4}}\text{C}\,{{\text{m}}^{-1}}\]as shown in the figure, such that the negative charge is at a distance of 2.0 cm from the line charge. The force acting on the dipole will be
The velocity \[v(\text{m}{{\text{s}}^{-1}})\]versus time graph of a body moving in a straight line is shown in figure. The displacement of the body in 5 s is
n batteries are connected to form a circuit as shown in the figure. The resistances denote the internal resistances of the batteries which are related to the emfs as \[{{r}_{i}}=k{{\varepsilon }_{i}}\], where k is a constant with proper SI units. The solid dots represent the terminals of the batteries. Then
A)
the current through the circuit is\[\frac{n}{k}\].
doneclear
B)
the potential difference between the terminals of the 1st battery is zero.
doneclear
C)
the current through the circuit is \[\frac{{{n}^{2}}}{k}\].
doneclear
D)
the potential difference between the terminals of the / battery is\[\frac{\varepsilon }{k}\].
A body of mass 0.5 kg travels in a straight line with velocity \[v=a{{x}^{3/2}}\]where \[a=5\,{{m}^{-1/2}}{{s}^{-1}}\]. The work done by the net force during its displacement from x = 0 to x = 2 m is
In figure, the coefficient of friction between the floor and the block B is The coefficient of friction between the blocks B and A is 0.2. The mass of A is m/2 and that of B is m. What is the maximum horizontal force F can be applied to the block B so that two blocks move together?
A vertical circular coil of radius 0.1 m and having 10 turns carries a steady current. When the plane of the coil is normal to magnetic meridian, a neutral point is observed at the centre of the coil. If \[{{B}_{H}}=0.314\times {{10}^{-4}}T\], then current in the coil is
A straight horizontal conducting rod of length 50 cm and mass 50 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero? (Take\[g=10\,\text{m}\,{{\text{s}}^{-2}}\])
A uniform disc of radius -R lies in x-y plane with its centre at origin. Its moment of inertia about the axis x = 2R and y = 0 is equal to the moment of inertia about the axis y = d and z = 0, where d is equal to
A uniform magnetic field B exists in a direction perpendicular to the plane of a square frame made of copper wire. The wire has a diameter of 2 mm and a total length of 40 cm. The magnetic field changes with time at a steady rate \[dB/dt=0.02\text{ }T\text{ }{{s}^{-}}^{1}\]. What will be the current induced in the frame? (Resistivity of copper \[=1.7\times {{10}^{-}}^{8}\Omega .m)\])
An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (r.m.s.), 50 Hz ac supply, the series inductor needed for it to work is close to
A satellite is moving in a circular orbit at a certain height above the earths surface. It takes \[5.26\times {{10}^{3}}\] s to complete one revolution with a centripetal acceleration equal to \[9.32\,m\,{{\text{s}}^{-2}}\]. The height of the satellite orbit above the earths surface is (Radius of earth \[=6.37\times {{10}^{6}}m\])
In a single slit diffraction pattern, the distance between the first minimum on the left and the first minimum on the right is 5 mm. The screen on which the diffraction pattern is displayed is at a distance of 80 cm from the slit. The wavelength is \[\text{6000}\overset{\text{o}}{\mathop{\text{A}}}\,\]. The slit width (in mm) is about
A slab of a material of refractive index 2 is shown in figure has a curved surface APB of radius of curvature 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in the figure. An object O is placed at a distance of 15 cm from the pole P as shown. The distance of the final image of O from P, as viewed from the left is
In a common emitter configuration of a transistor, the voltage drop across a \[500\Omega \] resistor in the collector circuit is 0.5 V when the collector supply voltage is 5 V. If the current gain in the common base mode is 0.96, the base current is
A pan pizza cools from \[91{}^\circ C\] to \[79{}^\circ C\] in 2 minutes, on a summer day, when the room temperature is \[25{}^\circ C\]. How long will the pan pizza takes to cool from \[91{}^\circ C\] to \[79{}^\circ C\], on a winter day, when the room temperature is \[5{}^\circ C\]?
The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is
Determine the period of small oscillations of a mathematical pendulum, that is a ball suspended by a thread l = 20 cm in length, if it is located in a liquid whose density is three times less than that of the ball. The resistance of the liquid is to be neglected.
A message signal of frequency 10 kHz and peak value of 10 volts is used to modulate a carrier of frequency 1 MHz and peak voltage 20 volts. The modulation index and side bands produced are
A particle is projected at an angle of \[60{}^\circ \] above the horizontal with a speed of \[10\text{m}{{\text{s}}^{-1}}\]. After some time, the direction of its velocity makes an angle of \[30{}^\circ \] above the horizontal. The speed of the particle at this instant is \[\frac{2n}{\sqrt{3}}\text{m}\,{{\text{s}}^{-1}}\]. The value of n is ____.
A bus is moving with a velocity of \[\text{5}\,\text{m}\,{{\text{s}}^{-1}}\]towards a huge wall. The driver sounds a horn of frequency 165 Hz. If the speed of sound in air in 335 \[\,\text{m}\,{{\text{s}}^{-1}}\], the number of beats per second heard by the passengers in the bus would be _____.
The ground state energy of hydrogen atom is \[-13.6\text{ }eV.\] The photon emitted during the transition of electron from n = 3 to n = 1 state, is incident on a photosensitive material of unknown work function. The photoelectrons are emitted from the materials with a maximum kinetic energy of 9 eV. The threshold wavelength of the material used is ____\[\overset{\text{o}}{\mathop{\text{A}}}\,\].
There is a stream of neutrons with a kinetic energy of 0.0327 eV. If the half-life period of neutrons is 700 s, the fraction of neutrons decay before they travel a distance of 5 m is \[x\times {{10}^{-8}}\]. The value of x is _____.
Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is 36 g and its density is \[9g\,c{{m}^{-3}}\]. If the mass of the other is 48 g, its density is__ \[g\,c{{m}^{-3}}\].
The fraction of molecules in one mole of an ideal gas that have energies greater than two times the average kinetic energy at \[50{}^\circ C\]and \[100{}^\circ C\] is
Which of the following statement is/are CORRECT? \[K{{O}_{2}}\] finds use in breathing equiment and safeguards the user to breathe in oxygen generated internally in the apparatus without being exposed to toxic fumes outside. The supply of oxygen is due to
(I) slow decomposition of \[K{{O}_{2}}\]
(II) reaction of \[K{{O}_{2}}\] with \[C{{O}_{2}}\] in the exhaled air
(III) reaction of \[K{{O}_{2}}\] with moisture in the essential air
The transition from state \[n=4\]to \[n=3\]in a \[H{{e}^{\oplus }}\]ion result in ultraviolet radiation. Infrared radiation will be obtained in the transition from
Increasing amount of solid \[Hg{{I}_{2}}\] is added to 1 L of an aqueous solution containing\[0.1\text{ }mol\text{ }KI\]. Which of the following graphs do represent the variation of freezing point of the resulting with the amount of \[Hg{{I}_{2}}\] added?
\[526.3\text{ }mL\]of \[0.5\text{ }mL\]\[HCl\] is shaken with \[0.5\text{ }g\]of activated charcoal and filtered. The concentration of the nitrate is reduced to \[0.4\text{ }m\]. The amount of adsorption \[(x/m)\] is
A heated iron block at \[127{}^\circ C\]loses \[300\text{ }J\]of heat to the surrounding which is at a temperature of\[27{}^\circ \]. \[\Delta S\]for this process is \[0.05x\,J\,{{K}^{-1}}.\]Find the value of x.
An acid solution of \[0.2\text{ }mol\]of \[K\operatorname{Re}{{O}_{4}}\]was reduced with \[Zn\]and then titrated with \[1.6\text{ }Eq\]of acidic \[KMn{{O}_{4}}\] solution. For the reoxidation of all the Rhenium \[(\operatorname{Re})\] to the Perrhenate ion \[({{\operatorname{ReO}}_{4}}^{\Theta })\]. Assuming that rhenium was the only element reduced. The oxidation state to which rhenium was reduced by \[Zn\]is ______.
One mole of \[{{N}_{2}}{{O}_{4}}(g)\] at \[100\text{ }K\]is kept in a closed container at \[1.0\text{ }atm\]pressure. It is heated to \[300\text{ }K,\] where 30% by mass of \[{{N}_{2}}{{O}_{4}}(g)\] decomposes to \[N{{O}_{2}}(g)\]. The resultant pressure is .___.
The moles of \[NaOH\]can be added to \[1.0\text{ }L\]of solution of \[0.1\text{ }M\]\[N{{H}_{3}}\] and \[0.1\text{ }M\]\[N{{H}_{4}}Cl\] without changing \[pOH\]by more than one unit (\[p{{K}_{a}}\] of \[N{{H}_{3}}=4.75\]) is ______.
The minimum value of the function \[\operatorname{f}(x)=\,\,{{x}^{3/2}}+\,\,x{{\,}^{-3/2}}\,-4\left( x+\frac{1}{x} \right)\] for all permissible real x, is
The line \[\operatorname{y} = mx\] bisects the area enclosed by lines \[\operatorname{x} =0\], \[\operatorname{y} = 0 and x = 3/2\] and the curve \[\operatorname{y} = 1 + 4x - {{x}^{2}}\]. Then the value of m is
If \[\operatorname{y}=2x\] is a chord of the circle \[{{\operatorname{x}}^{2}}+{{y}^{2}}= 10 x\], then the equation of the circle whose diameter is this chord, is-
Magnitudes of vectors \[\vec{a}, \vec{b}, \vec{c}\] are 3, 4, 5 respectively. If \[\vec{a}\] and \[\vec{b}\,+ \vec{c}\], \[\vec{b}\] and \[\vec{c}\,+\vec{a}\], \[\vec{c}\] and \[\vec{a}+\vec{b}\] are mutually perpendicular, then magnitude of \[\vec{a} +\vec{b}\,+\vec{c}\] is
If \[{{I}_{1}}=\int\limits_{0}^{1}{{{2}^{{{x}^{2}}}}dx},\,\,{{I}_{2}}=\int\limits_{0}^{1}{{{2}^{{{x}^{3}}}}dx}\], \[\int\limits_{1}^{2}{{{2}^{{{x}^{2}}}}dx}\] and \[{{I}_{4}}=\int\limits_{1}^{2}{{{2}^{{{x}^{3}}}}dx}\] then
If \[\operatorname{f}:R\to R\] and \[g:R\to R\] are defined by \[f(x)=\left| x \right|\] and \[g(x)=\left[ x-3 \right]\] for \[x\in R\] then \[\left\{ g(f(x)):-\frac{8}{5}<x<\frac{8}{5} \right\}\] is equal to
If PQ is a double ordinate of hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] such that OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies
The equation of the lines on which the perpendiculars from the origin make \[30{}^\circ \] angle with x-axis and which form a triangle of area \[\frac{50}{\sqrt{3}}\]with axes, are