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a.  A force of 50N is applied to the input piston of a hydraulic system the area of the input piston’s 60 cm2, and that of the output piston’s 15 cm2. (a) How much force does the output piston expert? (b) If the input piston moves 2.0cm per stroke, how far does the output piston move?


Replace the force system by an equivalent



A pulley is mounted on a frictionless axis and then the pulley is attached to the

higher end of the inclined surface as shown in the figure. A massless cord is

wrapped around the pulley while its other end is tied to a 1.0 kg object. The pulley

has a radius of 20 cm and moment of inertia of 0.4 kg m2


. The angle of the surface is 37° and the coefficient of kinetic friction is 0.2. The object is released from rest. The pulley starts to rotate as the object moves and the cord unwinds.

Determine the acceleration of the object and the tension in the cord.


What is meant by surface tension and surface energy? Show that the surface tension of a liquid is equal to the mechanical part of its energy. Show that the difference in pressure between the inside and outside of a spherical liquid drop is 2T/r , where T is the surface tension of the liquid, r is the radius of the spherical liquid drop.
What are meant by streamline motion and turbulent motion? Discuss the various forms of energy possessed by a liquid in motion. A small spherical steel ball of radius a of a material of density à   falls from rest in still air of viscosity à Ž ·. Now (i) Write up the equation of motion of the ball, (ii) Estimate its terminal velocity, and (iii) Find out the time and distance traversed when the ball has acquired 90% of the terminal velocity.
What is meant by elasticity? Explain the elastic and plastic materials. Name the four elastic constants, and explain what they mean. Establish the expressions to show how they are related to each other for an isotropic medium. What is meant by Poisson’s ratio? Compute its limiting values.
What is meant by acceleration due to gravity? Discuss the variation of acceleration due to gravity with (i) altitude, (ii) depth, and (iii) rotation of the earth. Define the escape velocity. Calculate the expression of the escape velocity.
Explain the Kepler’s laws of planetary motion and hence derive the Newton’s law of gravitation from the Kepler’s law. Show that Kepler’s law obeys the principle of conservation momentum. Obtain the expression for the gravitational potential and gravitational field due to a uniform solid sphere at a point (i) inside the sphere and (ii) outside the sphere
Explain the plane progressive wave. Define the energy density and energy current of a plane progressive wave. Obtain the expressions for the energy density and intensity of a plane progressive wave. When a plane progressive wave is propagated through a medium, the displacement of the particle (in cm) at any instant of time is given by, y=10sin2π/100(3600t-20) Calculate (i) the amplitude, (ii) wave velocity (iii) wavelength (iv) frequency, and (v) time period.
A damped harmonic oscillator is subjected to a sinusoidal driving frequency whose frequency is altered but amplitude kept constant. It is found that the amplitude of the oscillator increases from 0.02 mm at very low driving frequency to 8.00 mm at a frequency of 100 cps. Obtain the value of (i) quality factor (ii) the relaxation time, (iii) the damping factor.
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