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From a certain apparatus, the diffusion rate of hydrogen has an average value of 28.7 `cm^3` `s^(–1)`. The diffusion of another gas under the same conditions is measured to have an average rate of 7.2 `cm^3` `s^(–1)`. Identify the gas. [Hint : Use Graham’s law of diffusion: R1/R2 = ( M2 /M1 )1/2, where R1, R2 are diffusion rates of gases 1 and 2, and M1 and M2 their respective molecular masses. The law is a simple consequence of kinetic
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Given below are densities of some solids and liquids. Give rough estimates of the size of their atoms : [Hint : Assume the atoms to be ‘tightly packed’ in a solid or liquid phase, and use the known value of Avogadro’s number. You should, however, not take the actual numbers you obtain for various atomic sizes too literally. Because of the crudeness of the tight packing approximation, the results only indicate that atomic sizes are in the range of a few
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On an average, a human heart is found to beat 75 times in a minute. Calculate its frequency and
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A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period
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Given below are some examples of wave motion. State in each case if the wave motion is transverse, longitudinal or a combination of both: (a) Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways. (b) Waves produced in a cylinder containing a liquid by moving its piston back and forth. (c) Waves produced by a motorboat sailing in water. (d) Ultrasonic waves in air produced by a vibrating quartz
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For the wave described in Exercise 15.8, plot the displacement (y) versus (t) graphs for x = 0, 2 and 4 cm. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase
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A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 40 kHz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.03 times the speed of sound in air. What frequency does the bat hear reflected off the wall
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Explain why Hydrostatic pressure is a scalar quantity even though pressure is force divided by
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A vertical off-shore structure is built to withstand a maximum stress of `10^9` Pa. Is the structure suitable for putting up on top of an oil well in the ocean ? Take the depth of the ocean to be roughly 3 km, and ignore ocean
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During blood transfusion the needle is inserted in a vein where the gauge pressure is 2000 Pa. At what height must the blood container be placed so that blood may just enter the vein ? [Use the density of whole blood from Table
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Read the following two statements below carefully and state, with reasons, if it is true or false. (a) The Young’s modulus of rubber is greater than that of steel; (b) The stretching of a coil is determined by its shear
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Two uniform solid spheres of equal radii R, but mass M and 4 M have a centre to centre separation 6 R, as shown in Fig. . The two spheres are held fixed. A projectile of mass m is projected from the surface of the sphere of mass M directly towards the centre of the second sphere. Obtain an expression for the minimum speed v of the projectile so that it reaches the surface of the second sphere.
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The planet Mars has two moons, phobos and delmos. (i) phobos has a period 7 hours, 39 minutes and an orbital radius of `9.4 ×10^3` km. Calculate the mass of mars. (ii) Assume that earth and mars move in circular orbits around the sun, with the martian orbit being 1.52 times the orbital radius of the earth. What is the length of the martian year in days
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A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero ? Mass of the sun = `2×10^(30)` kg, mass of the earth = `6×10^(24)` kg. Neglect the effect of other planets etc. (orbital radius = `1.5 × 10^(11)`
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A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system ? Mass of the space ship = 1000 kg; mass of the sun = `2×10^(30)` kg; mass of mars = `6.4×10^(23)` kg; radius of mars = 3395 km; radius of the orbit of mars = `2.28 ×10^8` km; G = `6.67 × 10^(–11)` N `m^2`
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Show that the angular momentum about any point of a single particle moving with constant velocity remains constant throughout the
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(a) A child stands at the center of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value ? Assume that the turntable rotates without friction. (b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic
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A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and
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Fig. shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P
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The equation of motion of a particle is `x = a cos (α t )^ 2` . The motion
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