Suppose you have two coins which appear identical in your pocket. You know that, one is fair and one is 2-headed. If you take one out, toss it and get a head, what is the probability that it was a fair coin ?

Each phase of a material can exits only in certain regions of pressure and temperature . P-T phase diagrams, in which pressure is plotted versus temperature, show the regions corresponding to various phases and phase transformations . P-V diagrams, on the other hand , can be used to study pressure volume relationship at a constant temperature. If the liquid and gaseous phases of a pure substances are heated together in a closed container, both the temperature and the vapor pressure will increase until a point is reached at which the two phases can no longer be distinguished from one another. The temperature and pressure at which this occurs are called the critical temperature and pressure. Exceeding either of these parameters, by itself ,will cause the "gas"//"liguid" phase transition to disappear. if the other variable is then changed as well, while the first variable is maintained above its critical point , a gradual transition will occur between the gaseous and liquid phases, with no clear boundary.(The liquid and solid phases, on the other hand , maintain a distinct boundary at all pressure above the triple point). Shown in figure is a combined P-T phase diagram for material A and B . Which is true about the substance in figure?

Each phase of a material can exits only in certain regions of pressure and temperature . P-T phase diagrams, in which pressure is plotted versus temperature, show the regions corresponding to various phases and phase transformations . P-V diagrams, on the other hand , can be used to study pressure volume relationship at a constant temperature. If the liquid and gaseous phases of a pure substances are heated together in a closed container, both the temperature and the vapor pressure will increase until a point is reached at which the two phases can no longer be distinguished from one another. The temperature and pressure at which this occurs are called the critical temperature and pressure. Exceeding either of these parameters, by itself ,will cause the "gas"//"liguid" phase transition to disappear. if the other variable is then changed as well, while the first variable is maintained above its critical point , a gradual transition will occur between the gaseous and liquid phases, with no clear boundary.(The liquid and solid phases, on the other hand , maintain a distinct boundary at all pressure above the triple point). Shown in figure is a combined P-T phase diagram for material A and B . If heat is added to solids A and B , each in a container that is open to the atmosphere :-

A 100g block is connected to a horizontal massless spring of force constant 25.6 N//m . The block is free to oscillate on a horizontal fricationless surface. The block is displced by 3 cm from the equilibrium position, and at t = 0 , it si released from rest at x = 0 , The position-time graph of motion of the block is shown in figure. Let us now make a slight change to the initial conditions. At t = 0 , let the block be released from the same position with an initial velocity v_(1) = 64 cm//s . Position of the block as a function of time can be expressed as

Two different types of rubber are found to have the stress-strain curves shown in fig. (a) In which significant ways do these curves differ form the stress-strain curve of a metal wire. (b) A heavy machine is to be installed in a factory. To absorb vibrations of the machine, a block of rubber is placed between the machinery and the floor. which of the two rubbers A and B would you perfer to use for this purpose? why? (c) Which of the two rubber materials would you choose for a car tyre ?

A vessel contains two immiscible liquids of density rho_(1)=1000 kg//m^(3) and rho_(2)=1500kg//m^(3) . A solid block of volume V=10^(3)m^(3) and density d=800kg//m^(3) is tied to one end of a string and the outer end is tied to the bottom of the vessel as shown in figure. The block is immersed with two fifths of its volume in the liquid of lower density. The entire system is kept in an elevator which is moving upwards with an acceleration of a=g/2 . Find the tension in the string.

Consider a coin of Question 20. It is electrically neutral and contains equal amounts of positive and negative charge of magnitude 34.8 kC. Suppose that these equal charges were concentrated in two point charges separated by: (i) 1 cm (-1/2) xx displacement of the one paisa coin) (ii) 100 m (-length of a long building) (iii) 10^(6) m (radius of the earth). Find the force on each such point charge in each of the three cases. What do you conclude from these results ?

Two blocks of mass m_(1)=10kg and m_(2)=5kg connected to each other by a massless inextensible string of length 0.3m are placed along a diameter of the turntable. The coefficient of friction between the table and m_(1) is 0.5 while there is no friction between m_(2) and the table. the table is rotating with an angular velocity of 10rad//s . about a vertical axis passing through its center O . the masses are placed along the diameter of the table on either side of the center O such that the mass m_(1) is at a distance of 0.124m from O . the masses are observed to be at a rest with respect to an observed on the tuntable (g=9.8m//s^(2)) . (a) Calculate the friction on m_(1) (b) What should be the minimum angular speed of the turntable so that the masses will slip from this position? (c ) How should the masses be placed with the string remaining taut so that there is no friction on m_(1) .