Type the correct answer in each box. spell all words correctly. the part labeled a is a , and the part labeled b is a they did not offer options, by the way.

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Holes drilled several kilometers into earth’s crust provide direct evidence about earth’s interior in the form of

69. air frictionthe velocity of the satellitea. decreases b. increases c. sometimes increases sometimedecreases d. no effect at all70. the unit of gravitational potential energy isa.jouté b.watt c. newtond.pascal71. which of the following is not influenced by a magneta. cobalt b.copper c.irond. nickel72. one joule of work done in one second by unit positive chargea.1 watt b.1 volt c.1 js d. none73. the most deviated colour of light after passing through a prisea. violet b.red c. green d.yellow4. a coin is placed below a beaker fill with water upto 12 cm isdisplaced by water isa. 9cm b.6cmс.3cmd.7cm