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Q1. A ball is thrown from a point in level with and at a horizontal distance S from the top of a tower of height A. How must the speed and angle of projection of the ball be related to S in order that the ball may just go grazing past the top edge of the tower? At what horizontal distance B from the foot of the tower does the ball hit the ground? For a given speed of projection, obtain an equation for finding the angle of projection so that B is at a minimum.
Q2. A particle is objected from the end B of a horizontal track Bc at a given angle a to the horizontal. After just grazing the vertices A, A' , A'' �. Of the triangles BAC,BA'C, BA''C,�. On its way, it lands up at the point C on the other end of the horizontal line. Show that the sum of the tangents of the base angles of any of these triangles is a constant
Q3. A regular octagon stands vertically with one side in contact with a horizontal floor. A particle is projected from a point on floor at angle q with the horizontal such that it passes through the four vertices of the octagon. Show that q = cos 1 ( 1 / �7) . What is the horizontal range of this projectile?
Q4. An 'insect' on the axle of a wheel 'observes' the motion of a point on the rim of the wheel and 'finds' it to take its place along the circumference of a circle of radius R with a uniform angular speed w. The axle is moving with a uniform speed V relative to the ground. How will an observer on the ground describe the motion of the same point?
Q5. A projectile aimed at a mark which is in the horizontal plane through the point of projection falls a cm short of it when the elevation is b show that if the velocity of projection is same in all the cases, the proper elevation is
� sin2 [ a sin 2a + b sin 2b / (a+b) ]
Q6. An object is first sliding down an inclined plane of inclination q with constant velocity v. It is next projected up the plane with an initial velocity u. Calculate the distance upto which it will rise before coming to rest. What will happen to the object after it has come to rest?
Q7. 1 gram 226Ra is placed in an executed tube whose volume is 5cc.Assuming that each Ra nucleus yields four He atoms which are retained in the tube, what will be the partial pressures at 27�C of He produced at the end of a year?t1/2 for Ra is 1590 years
Q8. A mixture of Pu239 and Pu240 has a specific gravity of 6.0x109 dis/sec. The t1/2 of the isotopes are 2.44x104 and
6.58 x103 years. Calculate isotopic composition of the sample.(1yr = 3.15x107 sec)
Q9.What electronic transition in the He+ would emit the radiation of the same wavelength as that of the first Lyman transition of hydrogen(i.e., for an electron jumping from n=2 to n=1)? Neglect the reducedmass effect. Also calculate second ionization potential of He and first Bohr orbit for He+.
Q10. With what velocity should an aparticle travel towards the nucleus of a Cuatom so as to arrive at a distance 1013 metre from the nucleus of the Cuatom
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