Question

A block of mass $1\text{kg}$ and density $0.8{\text{g/cm}}^3$ is held stationary with the help of a string as shown in figure. The tank is filled with water such that the block is completely submerged in water. The tank is accelerating vertically upwards with an acceleration $a=1.0{\text{m/s}}^2$. Find the tension in the string.

• A. $2.75\text{N}$
• B. $3.5\text{N}$
• C. $5.15\text{N}$
• D. $6.8\text{N}$

Answer 1

The correct option is A $2.75\text{N}$

Free body diagram of the block is as shown below.



In the figure, $F$ is the upthrust force

$F=V_{\text{block}}{\rho }_w(g+a)$

$=\left(\frac{\text{mass of block}}{\text{density of block}}\right){\rho }_w(g+a)$

$=\left(\frac{1}{800}\right)\left(1000\right)(10+1)=13.75\text{N}$

And, $W=mg=10\text{N}$

Equation of motion of the block is,
$F-T-W=ma$
$13.75-T-10=1\times 1$
$\therefore T=2.75\text{N}$

Hence, $\left(A\right)$ is the correct answer.

Why this Q? In case of a container containing fluid is accelerating in vertical direction, Upthrust force= (volume of liquid displaced)X(density of liquid)X(effective gravity)