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A Carnot engine absorb `6×10^5` cal at `227^oc` calculate work done per cycle by the engine if it sink is at
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A steam engine delivers `5.4×10^8`J of work per minute and services `3.6 × 10^9`J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per
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A cylinder of fixed capacity 44.8 litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by 15.0 °C ? (R = 8.31 J `mol^(–1) K^(–1)`).Example
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A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 20 °C = 343 m
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A train, standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air. (i) What is the frequency of the whistle for a platform observer when the train (a) approaches the platform with a speed of 10 m `s^(–1)`, (b) recedes from the platform with a speed of 10 m `s^(–1)`? (ii) What is the speed of sound in each case ? The speed of sound in still air can be taken as 340 m
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At a depth of 1000 m in an ocean (a) what is the absolute pressure? (b) What is the gauge pressure? (c) Find the force acting on the window of area 20 cm × 20 cm of a submarine at this depth, the interior of which is maintained at sealevel atmospheric pressure. (The density of sea water is `1.03 × 10^3` kg `m^(-3)`, g = 10 m
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(a) It is known that density ρ of air decreases with height y as `ρ = ρ_0e^((-y)/y_0)` where `ρ_0`= 1.25 kg `m^(–3)` is the density at sea level, and `y_0` is a constant. This density variation is called the law of atmospheres. Obtain this law assuming that the temperature of atmosphere remains a constant (isothermal conditions). Also assume that the value of g remains constant. (b) A large He balloon of volume 1425 `m^3` is used to lift a payload of 400 kg. Assume that the balloon maintains constant radius as it rises. How high does it rise ? [Take
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Which of the following statements is/are true for a simple harmonic
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India has had a long and unbroken tradition of great scholarship — in mathematics, astronomy, linguistics, logic and ethics. Yet, in parallel with this, several superstitious and obscurantistic attitudes and practices flourished in our society and unfortunately continue even today — among many educated people too. How will you use your knowledge of science to develop strategies to counter these attitudes
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We measure the period of oscillation of a simple pendulum. In successive measurements, the readings turn out to be 2.63 s, 2.56 s, 2.42 s, 2.71s and 2.80 s. Calculate the absolute errors, relative error or percentage
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The unit of length convenient on the nuclear scale is a fermi : 1 f = `10^(–15)` m. Nuclear sizes obey roughly the following empirical relation : `r=r_oA^(1/3)` where r is the radius of the nucleus, A its mass number, and `r_o` is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise.
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A physical quantity X is related to four measurable quantities a, b, c and d as follows:`X = a ^2 b ^3 c ^(5/2) d^(–2)`. The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4%, respectively. What is the percentage error in quantity X ? If the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the
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In an experiment to estimate the size of a molecule of oleic acid 1 mL of oleic acid is dissolved in 19 mL of alcohol. Then 1 mL of this solution is diluted to 20 mL by adding alcohol. Now 1 drop of this diluted solution is placed on water in a shallow trough. The solution spreads over the surface of water forming one molecule thick layer. Now, lycopodium powder is sprinkled evenly over the film and its diameter is measured. Knowing the volume of the drop and area of the film we can calculate the thickness of the film
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Match the Column I (nam e of physicists) with Column II (contribution/discovery) and select the correct option from the codes given below. Column I Column II A. Johannes Kepler P. Nuclear model of the atom B. Tycho Brahe q. Planetary motion C. Nicolaus Copernicus r. Elliptical orbit theory D. Ernest Rutherford s. Circular orbit theory
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Assertion: Matter can neither be created nor be destroyed. Reason: This is law of definite
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All engineering phenomena deal with definite and measured quantities and so depend on the making of the measurement. We must be clear and precise in making these measurements. To make a measurement, magnitude of the physical quantity (unknown) is compared.The record of a measurement consists of three parts, i.e. the dimension of the quantity, the unit which represents a standard quantity and a number which is the ratio of the measured quantity to the standard quantity.A device which is used for measurement of length to an accuracy of about `10^(-3)m`,
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Snehit starts from his home and walks 50 m towards north, then he turns towards east and walks 40 m and then reaches his school after moving 20 m towards south. Then, his displacement from his home to school
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Velocity of a body moving along a straight line with uniform acceleration a reduces by (3/4)th of its initial velocity in time t0. The total time of motion of the body till its velocity becomes zero
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Assertion: The maximum height of projectile is always 25% of the maximum range. Reason: For maximum range, projectile should be projected at
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Uniform Circular Motion When an object follows a circular path at a constant speed, the motion of the object is called uniform circular motion. The word uniform refers to the speed which is uniform (constant) throughout the motion. Although the speed does not vary, the particle is accelerating because the velocity changes its direction at every point on the circular track.The figure shows a particle P which moves along a circular track of radius `r` with a uniform speed `u`.A particle is revolving at 1200 rpm in a circle of radius 30 cm. Then, its acceleration
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