Tension under water

Classical Mechanics Level 4

Two blocks $A$ and $B$ are tied with strings under water, as shown. The density of $A$ is greater than water whereas that of $B$ is less than water. The tensions in the strings are $T_1$ and $T_2,$ respectively.

How will the tensions change if the whole setup starts accelerating in the upward direction?

T_1

increases,

T_2

decreases

T_1

decreases,

T_2

increases Both increase Both decrease

1 solution

Akshat Sharda
Feb 27, 2018

Let the buoyant force be $F_A$ on block $A$ and $F_B$ on block $B$ .

So, for block $A$ ,

$T_{1}=m_{A}g-F_{A}\Rightarrow T_{1}=m_{A}g-\rho V_{A}g$

And for block $B$ ,

$T_{2}=F_{B}-m_{B}g \Rightarrow T_{2}=\rho V_{B}g-m_B g$

Now we can see that both $T_1$ and $T_2$ are proportional to $g$ , when whole setup start accelerating upwards, $g$ changes to $g+a$ where acceleration of setup is $a$ . Therefore, tension in both increase.

Tension under water

1 solution

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