Question

A small metal sphere is falling through a viscous liquid. The variation of velocity (\(V\)) with time (\(t\)) is shown correctly in graph

• A. b
• B. a
• C. d
• D. c

Hint:

The sphere speeds up from rest and its speed levels off at terminal velocity.

Answer 1

The Correct Option is C

Step 1: Approach
Write Newton's second law and read off the shape.

Step 2: Equation
$m\dfrac{dv}{dt}=mg-F_B-6\pi\eta rv$. The right side is largest at $v=0$ and decreases as $v$ grows, vanishing at $v_T=\dfrac{mg-F_B}{6\pi\eta r}$.

Step 3: Shape
Slope of the graph is $dv/dt$. It is largest at $t=0$ where $v=0$, and tends to zero when $v\to v_T$. This gives a curve rising from the origin and levelling off: graph (d).

Step 4: Option
Graph (d) is listed as option (C).

Final Answer:
The speed grows from zero and levels off at terminal velocity, which is graph (d), option (C). \[ \boxed{\text{graph (d)}} \]