Question

Column I describe some situations in which a small object moves. Column II describes some characteristics of these
motions. Match the situation in Column I with the characteristics in Column II and indicate your answer by darkening
appropriate bubbles in the 4 4 matrix given in the ORS

Answer 1

A) The given velocity of the object is of form : $v=c_1\sqrt{c^2-x^2}$ where $c_1$ and $c_2$ are positive constants. This expression is similar to that of velocity of particle in simple harmonic motion that is $v=\omega \sqrt{A^2-x^2}$ where $\omega$ (angular frequency) and $A$ (amplitude) are positive constants. Therefore, option 1.
B) From the equation $v=-kx$, it can be concluded that if $v=0$ then $x=0$ that is object comes to rest at $x=0$. Thus, object starting from negative x value comes to rest at $x=0$, it's velocity (hence kinetic energy) decreases with time. Therefore, option 2 and 3.
C) From the reference frame of the observer in the elevator an constant force (pseudo force) acts on the object. Hence the motion of the object will remain simple harmonic. Therefore, option 1.
D) The velocity of the object $=2\sqrt{\frac{G{M}_e}{R}}=\sqrt{2}\sqrt{\frac{2G{M}_e}{R}}=\sqrt{2}{v}_e$
where $v_e$ is escape velocity.
As other forces are neglected the direction of motion of an object does not change and speed of the object keeps on decreasing. Therefore, option 2 and 3.