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Column - I describes some situations in which a small object moves. Column - II describes some characteristics of these motions. Match the situations in Column - I with the characteristics in Column - II {:("Column -I","Column -II"),("(A) The object moves on the axis under a conservative","(P) The object executes a simple"),("force in such a way that its ''speed'' and position''","harmonic motion."),("satisfy" v=c_(1)sqrt(c_(2)-x^(2))"where" c_(1) and c_(2) "are positive",),("constants.",),("(B) The object moves on the x-axis in such a way that","(Q) The object does not change its"),("its velocity and its displacement from the origin satisfy","direction"),("v=-kx, where k is a positive constant",),("(C ) The object is attached to one end of a mass-less","(R ) The kinetic energy of the object"),("spring of a given spring constant. The other end of the","keeps on decreasing"),("spring is attached to the ceilling of an elevator. Initially",),("everything is at rest. Teh elevator starts going upwards",),("with a constant acceleration a. The motion of the",),("object is observed from the elevator during the period",),("it maintains this acceleration",),("(D) The object is projected from the earth's surface","(S) The object can change its direction"),("vertically upwards with a speed" 2sqrt((GM_(e ))/(R_(e )))"where","only once".),(M_(e )"is the mass of the earth and" R_(e )"is the radius of the",),("earth Neglect forces from objects other than the earth.",):} |
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Answer» `v = omega sqrt(A^(2)-x^(2))` Where `omega` ands A are positive constants. The given above equation. HENCE the body executes. (b) If follows from equation v = -KX that v = 0 at x = 0, i.e. object comes to rest at `x = 0`. Thusof object starting from a NEGATIVE x valuescomes to rest x = 0 , its velocity (and hence kinetic energy) decrease with time. Hence correct choices are (q) are (r ). (c ) For an observer in the refrence frame of the elevator, a constant force acts on the object. This a pseudo force. Hence the motion of the object remains simple harmonic, which is choice (p). (d) Since the speed of the object is `sqrt(2)` time the escape velocity `(v_(e ) = sqrt(2GM_(e )//R_(e )))` the direction of motion of the object does not charge (since the force exerted by objects other than the earth are neglected) and the speed of the object keeps decreasing. Hence the correct choices are (q) and (r ). |
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