$g_{d}=g(1-d / R)$
$\frac{g}{4}=g(1-d / R)$
$\frac{d}{R}=3 / 4$
$a=3 R / 4$
variation with height
$g_{h}=g\left(1-\frac{2 h}{R}\right)$
$\frac{g}{4}=g\left(1-\frac{2 h}{R}\right)$
$\frac{2 h}{R}=\frac{3}{4}$
$h=\frac{3 R}{8}$
max distance $=a+h=\frac{3 R}{4}+\frac{3 R}{8}$
$=\frac{9 R}{8}$
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| Column $I$ | Column $II$ |
| $(A)$ The object moves on the $\mathrm{x}$-axis under a conservative force in such a way that its "speed" and "position" satisfy $v=c_1 \sqrt{c_2-x^2}$, where $\mathrm{c}_1$ and $\mathrm{c}_2$ are positive constants. | $(p)$ The object executes a simple harmonic motion. |
| $(B)$ The object moves on the $\mathrm{x}$-axis in such a way that its velocity and its displacement from the origin satisfy $\mathrm{v}=-\mathrm{kx}$, where $\mathrm{k}$ is a positive constant. | $(q)$ The object does not change its direction. |
| $(C)$ The object is attached to one end of a massless spring of a given spring constant. The other end of the spring is attached to the ceiling of an elevator. Initially everything is at rest. The 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. | $(r)$ The kinetic energy of the object keeps on decreasing. |
| $(D)$ The object is projected from the earth's surface vertically upwards with a speed $2 \sqrt{\mathrm{GM}_e / R_e}$, where, $M_e$ is the mass of the earth and $R_e$ is the radius of the earth. Neglect forces from objects other than the earth. | $(s)$ The object can change its direction only once. |
$(A)$ Remains stationary if there no friction between the paper and the ball
$(B)$ Moves to the left and starts rolling backwards, $i.e.$, to the left if there is a friction between the paper and the ball
$(C)$ Moves foward, $i.e.$ in the direciton in 'which the paper is pulled
Here, the correct statements is/are
