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(C) For a point mass $m$ falling vertically in a viscous medium,the forces acting on it are gravity ($mg$ downwards) and the viscous drag force ($kv$

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(C) For a point mass $m$ falling vertically in a viscous medium,the forces acting on it are gravity ($mg$ downwards) and the viscous drag force ($kv$ upwards).According to Newton's second law,the equation of motion is: $ma = mg - kv$.Thus,the acceleration is $a = g - (k/m)v$.At $t = 0$,$v = 0$,so the initial acceleration is $a = g$ (maximum).As the speed $v$ increases,the drag force $kv$ increases,which causes the acceleration $a$ to decrease.Eventually,the speed reaches a terminal velocity $v_t = mg/k$,where the acceleration $a$ becomes zero.Therefore,the speed $v$ increases from $0$ and approaches a constant value $v_t$,while the acceleration $a$ decreases from $g$ and approaches $0$.Comparing this with the given graphs,Graph $C$ correctly shows the speed $v$ increasing towards a constant value and the acceleration $a$ decreasing towards zero.

Column-$I$	Column-$II$
$(1)$ Newton's third law of motion	$(a)$ $\vec{F}_{12} = -\vec{F}_{21}$
$(2)$ Law of conservation of momentum	$(b)$ $\Delta \vec{p} = 0$
	$(c)$ $\vec{F}_{12} = \vec{F}_{21}$

Which of the following options correctly describes the variation of the speed $v$ and acceleration $a$ of a point mass falling vertically in a viscous medium that applies a force $F = -kv$,where $k$ is a constant,on the body? (Graphs are schematic and not drawn to scale)

Similar Questions

Match the items in Column-$I$ with those in Column-$II$.

Column-$I$ Column-$II$

$(1)$ Newton's third law of motion $(a)$ $\vec{F}_{12} = -\vec{F}_{21}$

$(2)$ Law of conservation of momentum $(b)$ $\Delta \vec{p} = 0$

$(c)$ $\vec{F}_{12} = \vec{F}_{21}$

In the given figure, the blocks $A$, $B$, and $C$ weigh $4 \ kg$, $6 \ kg$, and $8 \ kg$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is . . . . . . $N$. (Use $g = 10 \ m/s^2$)

In which of the following graphs,the total change in momentum is zero?

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