A diatomic molecule moving-at a speed u absorbs a photon of wavelength \[\lambda \] and then dissociates into two identical atoms. One of the atoms is found to be moving with a speed v in a direction perpendicular to the initial direction of motion of the molecule. Take mass of the molecule to be M and find the binding energy of the molecule. Assume that momentum of absorbed photon is negligible compared to that of the molecule.
After one second, the velocity of a projectile makes an angle of \[45{}^\circ \] with the horizontal. After another one second, it is travelling horizontally. The magnitude of its initial velocity and angle of projection are \[(g=10\,m/{{s}^{2}})\]
Two blocks of masses m and Mare joined with an ideal spring of spring constant k and kept on a rough surface as shown. The spring is initially unstretched and the coefficient of friction between the blocks and the horizontal surface is \[\mu \]. What should be the maximum speed of the block of mass M such that the smaller block does not move?
Four spheres of diameter la and mass M are placed with their centres on the four comers of a square of side b. Then the moment of inertia of the system about an axis along one of the sides of the square is
If the weight of a body in vacuum is W, and \[{{W}_{1}}\]and \[{{W}_{2}}\]are weights when it is fully immersed in liquids of specific gravities \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\] respectively, then the relation among W, \[{{W}_{1}}\] and \[{{W}_{2}}\] is
A thermally insulated piece of metal is heated under atmospheric pressure by the source providing constant power P, due to this its absolute temperature depends on time as \[T\left( t \right)={{T}_{0}}{{\left[ 1+K\left( t-{{t}_{0}} \right) \right]}^{1/4}}\]. Here K, \[{{T}_{0}}\] and \[{{t}_{0}}\] are constants. Then the heat capacity \[{{C}_{p}}(T)\] can be given by
A massless piston connected to a spring of spring constant k fits smoothly inside an L-shaped fixed glass tube as shown in the figure. The piston can slide without friction and without leakage of water. The cross sectional area of the tube is s and the density of the liquid is\[\rho \]. If the system is slightly disturbed from its equilibrium position, then the angular frequency of its small oscillations is (m is the total mass of liquid and the liquid is ideal.)
A parallel plate air capacitor has a capacitance C (Fig. 1). When it is half filled with a dielectric of dielectric constant 5 (Fig. 2), the percentage increase in the capacitance will be
Figure shows a potentiometer arrangement with \[{{R}_{AB}}=10\,\Omega \] rheostat of variable resistance x. For \[x=0,\] null deflection point is found at 20 cm from A. For unknown value of x null deflection point was at 30 cm from A, then the value of x is
A rod of length l. negligible resistance and mass m slides on two horizontal frictionless rails of negligible resistance by hanging a block of mass w; with the help of insulating massless string passing through fixed massless pulley (as shown). If a constant magnetic field B acts vertically upwards perpendicular to the plane of the figure, the terminal velocity of hanging mass is
A light ray is incident perpendicular on one face of a \[90{}^\circ \] prism and is total internally reflected at the glass-air interface. If the angle of reflection is \[45{}^\circ \], we conclude that (the refractive index of glass is n).
A current I flows in a long straight wire whose cross-section is in the shape of a thin quarter ring of radius R. Find the induction of the magnetic field (B) at point O on the axis.
Two coils 1 and 2 are mounted co-axially as shown in the figure. The resistance of the two coils are \[{{R}_{1}}\] and \[{{R}_{2}}\] and their self- inductances are \[{{L}_{1}}\] and \[{{L}_{2}},\] respectively. Switch S is closed at time \[t=0\] to connect the coil 1 to an ideal cell of emf V. It is observed that by the time current reaches its steady value in coil 1, the quantity of charge that flows m coil 2 is \[{{Q}_{0}}\]. Calculate the mutual inductance {M) between the two coils.
A travelling microscope can move vertically along a scale. It is focused at a mark O on the table and the reading on the vertical scale is\[{{r}_{1}}\]. Now a glass slab is placed over mark O and the microscope has to be moved up to bring the mark in focus again. This time the scale reads\[{{r}_{2}}\]. Lycopodium powder is spread over the top of the glass slab and the microscope is moved up once again to bring the powder particles in sharp focus. This time the vertical scale reads\[{{r}_{3}}\]. Find the refractive index of the material of the glass slab.
A conducting sphere of radius R carries a charge Q. It is enclosed by another concentric spherical shell of radius 2R. Charge from the inner sphere is transferred in infinitesimally small installments to the outer sphere. The work done in transferring the entire charge from the inner sphere to the outer one will be
In the figure, each segment (side of small triangle) has resistance R and the wire used in circumference of the circle has negligible resistance. Find the equivalent resistance between point O and A.
In Young's double slit experiment (with identical slits), the intensity of a maxima is I. P is a point on the screen where 10th maxima is formed with light of wavelength \[\lambda =6000\overset{o}{\mathop{A}}\,\]. Find the intensity at point P if the entire experimental set up is submerged in water of refractive index \[\mu =\frac{4}{3}\]. Assume that intensity due to individual slits remains unchanged after the system is dipped in water.
Following figure shows an ac generator connected to a "black box" through a pair of terminals. The box contains possible R, L, C or their combination, whose elements and arrangements are not known to us. Measurements outside the box reveals that \[e=75\sin (\sin \omega t)\]volt, \[i=1.5\sin (\omega t+45{}^\circ )\] amp, then the wrong statement is
Two bodies of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance r between them is
Power transmitted on a string by means of transverse wave has dimension formula represented by \[\frac{1}{2}\left[ {{\mu }^{1}}{{V}^{1}}{{\omega }^{x}}{{A}^{2}} \right]\]Find the value of x, if \[\mu \] is linear mass density \[(kg/m),V\] speed \[(m/s),\]\[\omega \] is angular frequency (rad/sec), A is amplitude (in metre).
Given \[{{m}_{A}}=30kg,\]\[{{m}_{B}}=10kg,\] \[{{m}_{C}}=20kg\] Between A and B \[{{\mu }_{1}}=0.3,\]between B and C \[{{\mu }_{2}}=0.2,\] and between C and ground \[{{\mu }_{3}}=0.1\]. What is the least horizontal force F (in N) to start motion of any part of the system of three blocks resting upon one another as shown in figure \[(g=10m/{{s}^{2}})\]
A siren placed at a railway platform is emitting sound of frequency\[5\text{ }kHz\]. A passenger sitting in a moving train A records a frequency of \[5.5\text{ }kHz,\] while the train approaches the siren. During his return journey in a different train, he records a frequency of \[6.0\text{ }kHz\]while approaching the same siren. What is the ratio of the velocity of train B to that of train A?
The distance advanced by a screw of a screw gauge is 2 mm in four rotations. Its cap is divided into 50 divisions. There is no zero error. If the screw reads 3 divisions on the main scale and 32 divisions on the cap, then find the diameter of the wire (in mm) is?
Two point objects A and B are kept on the principal axis of a convex lens as shown. Image of both the objects is formed at same position. Find the focal length of the lens (in cm)?
Identify Z in the following sequence of reactions - \[C{{H}_{3}}-COON{{H}_{4}}\xrightarrow{\Delta }X\xrightarrow{{{P}_{2}}{{O}_{5}}}Y\xrightarrow{{{H}_{2}}O/{{H}^{\oplus }}}Z\]
A solid has a structure in which 'W' atoms are located at the corners of a cubic lattice, 'O' atoms at the centre of edges and Na atoms at the centre of the cube. The formula for the compound is
One mole of \[NaCl\] (s) on melting absorbed \[30.5\text{ }kJ\]one of heat and its entropy is increased by \[28.8\,J{{K}^{-1}}mo{{l}^{-1}}\]. The melting point of \[NaCl\] is
The half-life for radioactive decay of C-14 is 5730 years. An archaeological artifact containing wood had only 80% of the C-14 found in a living tree. The age of the sample is
A metal crystallizes into a lattice containing a sequence of layers of atoms of ABABAB.......What percentage by volume of this lattice has empty space?
In an experiment, \[4\,g\]of \[{{M}_{2}}{{O}_{X}}\] oxide was reduced to \[2.8\text{ }g\]of the metal. Calculate the number of O atoms in the oxide. (Given: Atomic mass of the metal\[=56g\text{ }mo{{l}^{-1}}\])
If \[\sum\limits_{i=1}^{9}{({{x}_{i}}-5)=9}\] and \[\sum\limits_{i=1}^{9}{{{({{x}_{i}}-5)}^{2}}=45}\], then the standard deviation of the 9 items \[{{x}_{1}},{{x}_{2}},....,{{x}_{9}}\] is
If the eccentricity of \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is\[\frac{5}{4},\] then the eccentricity of \[\frac{{{x}^{2}}}{{{b}^{2}}}-\frac{{{y}^{2}}}{{{a}^{2}}}=1\] is
Let L be the line of intersection of the planes \[2x+3y+z=1\]and \[x+3y+2z=2\]. If L makes an angle\[\alpha \]with the positive x-axis, then \[\cos \alpha \] equals
If \[{{\log }_{x}}y,{{\log }_{z}}x,{{\log }_{y}}z\] are in G.P., xyz = 64 and \[{{x}^{3}},{{y}^{3}},{{z}^{3}}\] are in A.P, then x + y - z is ________.
Let \[\vec{a},\vec{b},\vec{c}\] be non-zero vectors such that \[(\vec{a}\times \vec{b})\times \vec{c}=\frac{1}{3}|\vec{b}||\vec{c}|\vec{a}\]. If \[\theta \] is the angle between \[\vec{b}\] and \[\vec{c}\], then \[\frac{\sin \left( \frac{\pi }{4} \right)}{\sin \theta }=\]_______.