Question

A solid sphere of mass $m = 2Kg$ and specific gravity $S = 0.5$ is held stationary relative to a tank filled with water. The tank is accelerating upward with acceleration $2m/{s^2}$. The tension in the string is found to be $8n$. Find the value of n? Given density of water $= 1000kg{m^{ - 3}}$ and $g = 10m/{s^2}$

A. 0
B. 1
C. 3
D. 5

Answer 1

The question talks about the performance of a solid submerged or immersed in a liquid, where the mass of the solid is taken note of and more so the density with respect to the volume of the surrounding liquid body.

Complete step by step answer: We are given a solid sphere of mass $m = 2Kg$ and specific gravity $S = 0.5$ is held stationary relative to the tank filled with water and the tank is accelerating upward with acceleration $2m/{s^2}$. The tension in the string is found to be $8n$.
We have to find the value of n.
Following the action of the solid in the water, where the weight of the solid is pointed to the water and since it is an upward and downward movement of the solid because of the reaction from the water.
The equation necessary to solve the question is $T = mg + ma$
On substituting all the given parameters into the equation, we get $8n = mg + ma$
Then $8n = m(g + a)$, where m is 2kg, g is $10m/{s^2}$ and acceleration is $2m/{s^2}$
$8n = 2(10 + 2) \\\ \Rightarrow 8n = 24 \\\ \Rightarrow n = \dfrac{{24}}{8} \\\ \Rightarrow n = 3 \\\$
Therefore, the correct option is Option C.

Note: The same process happens in objects like ships on water, submarines, ferries and boats and also to the motion of a person inside a lift or elevator where the person either acts towards gravity or is the same opposite to gravity. The sign convention has it that the minus or negative sign shows that acceleration due to gravity is away from the earth center while the plus or positive sign shows that it is acting towards the center of the earth.