A spherical ball is dropped from rest into a long column of a...

When the ball is dropped from rest, its initial velocity is zero. The viscous drag force is initially zero. The initial acceleration is at its maximum, determined by the effective weight (gravity minus buoyancy).

As the ball falls and gains velocity, the upward viscous drag force ($F_v = 6\pi\eta r v$) increases. The net downward force decreases, which means the acceleration decreases.

According to Newton's second law, $ma = W_{eff} - F_v$. Thus, $a = a_0 - \dfrac{6\pi\eta r}{m} v$.

Since velocity increases and approaches a constant terminal velocity asymptotically, the acceleration decreases and asymptotically approaches zero. Therefore, the acceleration-time graph is a curve starting from a positive maximum value on the y-axis and decreasing asymptotically to zero on the x-axis.

Answer: A curve starting from a positive maximum value on the acceleration axis and decreasing asymptotically to zero.