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A block of mass m sliding on a smooth horizontal surface with a velocity \[\vec{\nu}\] meets a long horizontal spring fixed at one end and with spring constant k, as shown in following figure following. Find the maximum compression of the spring. Will the velocity of the block be the same as \[\vec{\nu}\] when it comes back to the original position shown?
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A small block of mass 100 g is pressed against a horizontal spring fixed at one end to compress the spring through 5 cm (figure following). The spring constant is 100 N/m. When released, the block moves horizontally till it leaves the spring. Where will it hit the ground 2 m below the spring?
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A uniform ladder of length 10⋅0 m and mass 16⋅0 kg is resting against a vertical wall making an angle of 37° with it. The vertical wall is frictionless but the ground is rough. An electrician weighing 60⋅0 kg climbs up the ladder. If he stays on the ladder at a point 8⋅00 m from the lower end, what will be the normal force and the force of friction on the ladder by the ground? What should be the minimum coefficient of friction for the electrician to work safely?
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Suppose the friction coefficient between the ground and
the ladder of the previous problem is 0.540. Find the
maximum weight of a mechanic who could go up and do
the work from the same position of the ladder.
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The door of an almirah is 6 ft high, 1⋅5 ft wide and weighs 8 kg. The door is supported by two hinges situated at a distance of 1 ft from the ends. If the magnitudes of the forces exerted by the hinges on the door are equal, find this magnitude.
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The force of viscosity is
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The viscous force acting between two layers of a liquid is given by \[\frac{F}{A} = - \eta\frac{dv}{dz}\]. This F/A may be called
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A raindrop falls near the surface of the earth with almost uniform velocity because
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A spherical ball is dropped in a long column of a viscous liquid. The speed of the ball as a function of time may be best represented by the graph
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In discussing Doppler effect, we use the word "apparent frequency". Does it mean that the frequency of the sound is still that of the source and it is some physiological phenomenon in the listener's ear that gives rise to Doppler effect? Think for the observer approaching the source and for the source approaching the observer.
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The engine of a train sounds a whistle at frequency v. The frequency heard by a passenger is
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The change in frequency due to Doppler effect does not depend on
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Find the increase in pressure required to decrease the volume of a water sample by 0.01%. Bulk modulus of water = 2.1 × 109 N m−2.
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Estimate the change in the density of water in ocean at a depth of 400 m below the surface. The density of water at the surface = 1030 kg m−3 and the bulk modulus of water = 2 × 109 N m−2.
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A metal sphere of radius 1 mm and mass 50 mg falls vertically in glycerine. Find (a) the viscous force exerted by the glycerine on the sphere when the speed of the sphere is 1 cm s−1, (b) the hydrostatic force exerted by the glycerine on the sphere and (c) the terminal velocity with which the sphere will move down without acceleration. Density of glycerine = 1260 kg m−3 and its coefficient of viscosity at room temperature = 8.0 poise.
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Estimate the speed of vertically falling raindrops from the following data. Radius of the drops = 0.02 cm, viscosity of air = 1.8 × 10−4 poise, g= 9.9 × 10 ms−2 and density of water = 1000 kg m−3.
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Water flows at a speed of 6 cm s−1 through a tube of radius 1 cm. Coefficient of viscosity of water at room temperature is 0.01 poise. Calculate the Reynolds number. Is it a steady flow?
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A tightly closed metal lid of a glass bottle can be opened more easily if it is put in hot water for some time. Explain.
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A metal sheet with a circular hole is heated. The hole
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Two identical rectangular strips, one of copper and the other of steel, are riveted together to form a bimetallic strip (acopper> asteel). On heating, this strip will
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