A projectile is projected from a level ground making an angle \[\theta \] with the horizontal (x direction). The vertical (y) component of its velocity changes with its x co-ordinate according to the graph shown in figure. Calculate \[\theta \]. Take g \[g=10\,m{{s}^{-2}}\].
A man is running along a road with speed u. On his chest there is a paper of mass m and area S. There is a wind blowing against the man at speed V. Density of air is\[\rho \]. Assume that the air molecules after striking the paper come to rest relative to the man. The minimum coefficient of friction between the paper and the chest so that the paper does not fall is
Rectangular block B, having height h and width d has been placed on another block A as shown in the figure. Both blocks have equal mass and there is no friction between A and the horizontal surface. A horizontal time dependent force \[F=kt\]is applied on the block A. At what time will block B topple? Assume that friction between the two blocks is large enough to prevent B from slipping.
A section of fixed smooth circular track of radius R in vertical plane is shown in the figure. A block is released from position A and leaves the track at B. The radius of curvature of its trajectory when it just leaves the track at B is
A rope thrown over a pulley has a ladder with a man of mass m on one of its ends and a counterbalancing mass Mon its other end. The man climbs with a velocity v, relative to ladder. Ignoring the masses of the pulley and the rope as well as the friction on the pulley axis, the velocity of the centre of mass of this system is
Two particles A and B, each of mass m and moving with velocity v, hit the ends of a rigid bar of mass M and length simultaneously and stick to the bar. The bar is kept on a smooth horizontal plane (as shown). Find the angular speed of the system (bar + particle) after the collision. \[[M=6m]\]
Two solid conducting spheres of radii \[{{R}_{1}}\] and \[{{R}_{2}}\]are kept at a distance d (\[>>{{R}_{1}}\] and \[{{R}_{2}}\]) apart. The two spheres are connected by thin conducting wires to the positive and negative terminals of a battery of emf V. Find the electrostatic force between the two spheres.
Two simple harmonic motion \[{{x}_{1}}=a\sin \,\omega t\] and \[{{x}_{2}}=b\cos \,\omega t\] are superimposed on a particle. The displacements \[{{x}_{1}}\] and \[{{x}_{2}}\] are along the same directions. Then choose the correct option.
A)
The particle will not perform SHM.
doneclear
B)
The motion will not be oscillatory.
doneclear
C)
The particle will perform SHM.
doneclear
D)
The particle will perform periodic motion but not SHM.
A graph of the x-component of the electric field as a function of x in a region of space is shown. The y and z components of the electric field are zero in this region. If the electric potential is \[10\text{ }V\]at the origin, then potential at \[x=2.0\text{ }m\]is
An equilateral triangular loop ADC of uniform specific resistivity having some resistance is pulled with a constant velocity v out of a uniform magnetic field directed into the paper. At time \[t=0,\] side DC of the loop is at the edge of the magnetic field. The induced current (I) versus time (t) graph will be as
In Young's double slit experiment with light of wavelength \[K=600\text{ }nm,\]intensity of central fringe is \[{{I}_{0}}\]- One of the slits is covered by glass plate of refraction index \[1.4\] and thickness \[t=5\mu m,\] the new intensity at the same point on screen will be
The gates A, B, C and D shown in the diagram are OR gate, AND gate, AND gate and NOT gate respectively. Choose the correct relation between A, B and Y.
A particle is projected under gravity with velocity \[\sqrt{2ag}\] from a point at a height h above the level plane at an angle \[\theta \] to it. The maximum range R on the ground is
The block A of mass \[10\text{ }kg\]is kept on platform P of mass\[25\text{ }kg\]. A force of \[25\text{ }N\]is applied on P and force of \[10\text{ }N\]is applied on A as shown in the figure. Friction is absent between platform and ground. Coefficient of friction between platform and block is \[\mu =0.06.\] Direction of frictional force on block A will be
A)
Towards positive x-axis
doneclear
B)
Towards negative y- axis
doneclear
C)
At an angle of \[45{}^\circ \]from \[+x\] axis to-y axis
A ball collides elastically with a massive wall moving towards it with a velocity of v as shown. The collision occurs at a height of h above ground level and the velocity of the ball just before collision is 2v in horizontal direction. The distance between the foot of the wall and the point on the ground where the ball lands, at the instant the ball lands, will be
Two long straight cylindrical conductors with resistivities \[{{\rho }_{1}}\] and \[{{\rho }_{2}}\] respectively are joined together as shown in figure. If current I flows through the conductors, the magnitude of the total free charge at the interface of the two conductors is
A piece of conducting wire of resistance R is cut into \[2n\] equal parts. Half the parts are connected in series to form a bundle and remaining half in parallel to form another bundle. These bundles are then connected to give the maximum resistance. The resistance of the combination is
Eight equal drops of water are falling through air with a steady velocity of\[10\,\,cm{{s}^{-1}}\]. If the drops combine to form a single drop big in size. What is the terminal velocity of this big drop in (cm/sec)?
ABCDEF is a closed container like a prism placed such that face ACDE is lying horizontally. A liquid of uniform density is filled inside the container. Let \[{{F}_{1}}\] be the force due to liquid on the face ABC and \[{{F}_{2}}\] is the force on the face ABFE. What is the ratio of \[\frac{{{F}_{1}}}{{{F}_{2}}}\] ? (assume that pressure at line FB is zero)
The transverse displacement of a string is given by\[y(x,t)=0.06sin\left( \frac{2\pi }{3}x \right)\cos (120\pi t)\] where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 x 10~2 kg. Determine the tension in the string (in Newton).
A concave mirror forms a real image, on a screen of thrice the linear dimension of a real object placed on its principal axis. The mirror is moved by 10 cm along its principal axis and once again a sharp image of the object is obtained on the screen. This time the image is twice as large as the object. Find the focal length of the mirror (in cm).
In the circuit shown in figure, cell is ideal and\[{{R}_{2}}=100\,\Omega \]. A voltmeter of internal resistance \[200\,\Omega \]. reads \[{{V}_{12}}=4V\] and \[{{V}_{23}}=6V\]between the pair of points \[1-2\] and \[2-3\] respectively. What will be the reading of the voltmeter in (volt) between the points\[1-3\]?
The aqueous solution containing which one of the following ions will be colourless? (Atomic number: (\[\operatorname{Sc} = 21, Fe = 26\], \[\operatorname{Ti} = 22, Mn = 25)\]
A solution of urea \[\left( mol.\text{ }mass\text{ }56\text{ }g\text{ }mo{{l}^{-}}^{1} \right)\] boils at 100. \[18{}^\circ C\] at the atmospheric pressure. If \[{{K}_{f}}\,\,and\,\,{{K}_{b}}\] for water are 1.86 and 0.512 K kg \[mo{{l}^{-1}}\] respectively, the above solution will freeze at
For a chemical reaction \[\operatorname{A}\to Products\], the rate of disappearance of A is given by \[\frac{-d{{C}_{A}}}{dt}=\frac{{{k}_{1}}{{C}_{A}}}{1+{{k}_{2}}{{C}_{A}}}\] At very low\[{{C}_{A}}\], the reaction of the .......... order with rate constant........ (Assume \[{{k}_{1}},\,\,{{k}_{2}}\] are lesser than 1)
Atoms consists of protons, neutrons and electrons. If the mass of neutrons and electrons were made half and two times respectively to their actual masses, then the atomic mass of, \[_{6}{{C}^{12}}\]
A reaction proceeds by first order, \[75\,%\] of this reaction was completed in 32 min. What is the time (in minutes) required for \[50\,%\] completion?
The edge length of unit cell of a metal having molecular weight \[75\text{ }g\text{ }mo{{l}^{-}}^{1}is\text{ }5\overset{\text{o}}{\mathop{\text{A}}}\,\] which crystallizes in cubic lattice. If the density is 2 g/cc then find the radius of metal atom. \[(N=6\times 1{{0}^{23}})\]. Give the answer in pm.
In a polar molecule, the ionic charge is \[4.8\,\times 1{{0}^{-}}^{10}\] e.s.u. If the inter ionic distance is one A unit, then what is the dipole moment (in debye)
Calculate the mass of \[BaC{{O}_{\text{3}}}\] (in grams) produced when excess \[C{{O}_{2}}\] is bubbled through a solution of 0.205 mol \[Ba{{(OH)}_{2}}\].
Let r be the range of \[n(\forall n\ge 1)\] observations \[{{x}_{1}},{{x}_{2}},....,{{x}_{n}}\],if\[S=\sqrt{\frac{\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\overline{x})}^{2}}}}{n-1}}\]then
Three numbers are chosen at random without replacement from 1, 2, 3, ..., 10. The probability that the minimum of the chosen numbers is 4 or their maximum is 8 is
If \[\vec{a},\vec{b},\vec{c}\]are unit vectors, then \[|\vec{a}-\vec{b}{{|}^{2}}+|\vec{b}-{{\vec{c}}^{2}}+|\vec{c}-\vec{a}{{|}^{2}}\] does not exceed ___.