The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the
A strip of copper and another germanium are cooled from room temperature to 80 K. The resistance of
Formation of covalent bonds in compounds exhibits
Which part of a transistor is most heavily doped to produce large number of majority carriers?
The energy band gap is maximum in
By increasing the temperature, the specific resistance of a conductor and a semiconductor
At absolute zero, Si acts as
The period of revolution of a satellite orbiting Earth at a height 4R above the surface of Earth is x hrs, where R is the radius of earth. The period of another satellite at a height 1.5R from the surface of the Earth is
The value of acceleration due to gravity will be 1% of its value at the surface of earth at a height of (Re = 6400 km)
If the radius of earth shrinks to kR (k < 1), where R is the radius of Earth, then the time period of rotation of Earth, about its axis will become
A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is
A planet of radius R = 1/10 (radius of Earth) has the same mass density as Earth. Scientists dig a well of 10 depth R5 on it and lower a wire of the same length and of linear mass density 10–3 kg m–1 into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth = 6 × 106 m and the acceleration due to gravity on Earth is 10 ms–2)
A satellite is moving with a constant speed V in a circular orbit about the earth. An object of mass m is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is
The ratio between masses of two planets is 3 : 5 and the ratio between their radii is 5 : 3. The ratio between their acceleration due to gravity will be
If the radius of earth were to shrink by one percent and mass remains same, then acceleration due to gravity on the surface of the earth would
A planet is at R distance from sun and its time period of revolution is T. What will be its new time period of revolution if it is brought 0.5 R distance closer to sun?
The time period of a satellite of the earth is 10 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, then what will be the new time period of the satellite?
Which of the following layering pattern will have a void fraction of 0.26?
Lithium crystallizes in a body centred cubic lattice, how many next nearest neighbours does each Li has?
Quartz on strong heating followed by rapid cooling gives glass which is an amorphous solid because
F-centers are related to
Zinc sulphide exists in two different structural forms as zinc blende (FCC) and Wurtzite (HCP). What will be the coordination number of cation and anion in both the structures?
Density of crystal decreases in
A tetrahedral void in fcc is formed by atoms at
In a crystalline solid, anion B are arranged in cubic close packing and cation A are equally distributed between octahedral and tetrahedral voids. If all the octahedral voids are occupied, the formula for the solid is
An element (At. mass = 50 g/mol) having fcc structure has unit cell edge length 400 pm. The density of element is
In Zinc blende structure, Zn+2 ions are present in alternate tetrahedral voids and S–2 in ccp. The coordination number of Zn+2 and S–2 are respectively
The ratio of number of closed packed atoms to the number of tetrahedral holes in cubic closed packing is
If a cation leaves a site in solid lattice, and is located at an interstitial position. The lattice defect is
A binary solid has atoms B constitutes fcc lattice and atoms A occupies 25% of tetrahedral holes. The formula of solid is
Two physical pendulums perform small oscillations about the same horizontal axis with frequencies w1 and w2. Their moments of inertia relative to the given axis are equal to I1 and I2 respectively. In a state of stable equilibrium, the pendulums were fastened rigidly together. What will be the frequency of small oscillations of the compound pendulum?
A physical pendulum performs small oscillations about the horizontal axis with frequency co = 15.0 s-1 . When a small body of mass m = 50 g is fixed to the pendulum at a distance l = 20 cm below the axis, the oscillation frequency becomes equal to w2 = 10.0 s-1. Find the moment• of inertia of the pendulum relative to the oscillation axis.
A physical pendulum is positioned so that its centre of gravity
is above the suspension point. From that position the pendulum
started moving toward the stable equilibrium and passed it with an
angular velocity w. Neglecting the friction find the period of small
oscillations of the pendulum.
An arrangement illustrated in Fig consists of a horizontal uniform disc D of mass m and radius R and a thin rod AO whose torsional coefficient is equal to k. Find the amplitude and the energy of small torsional oscillations if at the initial moment the disc was deviated through an angle φ, from the equilibrium position and then imparted an angular velocity φo.
A uniform rod of mass m = 1.5 kg suspended by two identical threads 1 = 90 cm in length (Fig) was turned through a small angle about the vertical axis passing through its middle point C. The threads deviated in the process through an angle a = 5.0°.Then the rod was released to start performing small oscillations.Find:
(a) the oscillation period;
(b) the rod's oscillation energy.
A pendulum is constructed as a light thin-walled sphere of radius R filled up with water and suspended at the point 0 from a light rigid rod (Fig). The distance between the point 0 and the centre of the sphere is equal to 1. How many times will the small oscillations of such a pendulum change after the water freezes? The viscosity of water and the change of its volume on freezing are to be neglected.
A particle of mass m moves in the plane xy due to the force varying with velocity as F = a (yi — xj), where a is a positive constant,i and j are the unit vectors of the x and y axes. At the initial moment t = 0 the particle was located at the point x = y = 0 and possessed a velocity v0 directed along the unit vector j. Find the law of motion x (t) , y (t) of the particle, and also the equation of its trajectory.
Solve the foregoing problem for the case of the pan having a mass M. Find the oscillation amplitude in this case.
A body of mass m fell from a height h onto the pan of a spring balance (Fig.)The masses of the pan and the spring are negligible, the stiffness of the latter is x. Having stuck to the pan, the body starts performing harmonic oscillations in the vertical direction. Find the amplitude and the energy of these oscillations.
A particle of mass in moves due to the force F = - αmr,where a is a positive constant, r is the radius vector of the particle relative to the origin of coordinates. Find the trajectory of its motion if at the initial moment r = roi and the velocity v = voj, where I and j are the unit vectors of the x and y axes.
A mathematical pendulum oscillates in a medium for which the logarithmic damping decrement is equal to 20 = 1.50. What will be the logarithmic damping decrement if the resistance of the medium increases n = 2.00 times? How many times has the resistance of the medium to be increased for the oscillations to become impossible?
A body of mass in was suspended by a non-stretched spring, and then set free without push. The stiffness of the spring is x.Neglecting the mass of the spring, find:
(a) the law of motion y (t) , where y is the displacement of the body from the equilibrium position;
(b) the maximum and minimum tensions of the spring in the process of motion.
A plank with a body of mass m placed on it starts moving straight up according to the law y = a (1 — cos wt), where y is the displacement from the initial position w = 11 /s. Find:
(a) the time dependence of the force that the body exerts on the plank if a = 4.0 cm; plot this dependence;
(b) the minimum amplitude of oscillation of the plank at which the body starts falling behind the plank;
(c) the amplitude of oscillation of the plank at which the body springs up to a height h = 50 cm relative to the initial position (at the moment t = 0).
Find the time dependence of the angle of deviation of a mathematical pendulum 80 cm in length if at the initial moment the pendulum (a) was deviated through the angle 3.0° and then set free without push;
A plank with a bar placed on it performs horizontal harmonic oscillations with amplitude a = 10 cm. Find the coefficient of friction between the bar and the plank if the former starts sliding along the plank when the amplitude of scillation of the plank becomes less than T = 1.0 s.
In the arrangement shown in Fig the sleeve M of mass m=0.20 kg is fixed between two identical springs whose combined stiffness is equal to x = 20 N/m. The sleeve can slide without friction over a horizontal bar AB. The arrangement rotates with a constant angular velocity w = 4.4 rad/s about a vertical axis passing through the middle of the bar. Find the period of small oscillations of the sleeve. At what values of o will there be no oscillations of the sleeve?.
Imagine a shaft going all the way through the Earth from pole to pole along its rotation axis. Assuming the Earth to be a homogeneous ball and neglecting the air drag, find:
(a) the equation of motion of a body falling down into the shaft;
(b) how long does it take the body to reach the other end of the shaft;
(c) the velocity of the body at the Earth's centre
A uniform rod is placed on two spinning wheels as shown in Fig. The axes of the wheels are separated by a distance 1= 20 cm,the coefficient of friction between the rod and the wheels is k = 0.18. Demonstrate that in this case the rod performs harmonic oscillations. Find the period of these oscillations.
Determine the period of oscillations of mercury of mass = 200 g poured into a bent tube (Fig.) whose right arm forms an angle 0 = 30° with the vertical. The cross-sectional area of the tube is S = 0.50 cm2. The viscosity of mercury is to be neglected.
A small body of mass in is fixed to the middle of a stretched string of length 2l. In the equilibrium position the string tension is equal to To. Find the angular frequency of small oscillations of the body in the transverse direction. The mass of the string is negligible,the gravitational field is absent.