Question

A string is holding a solid block below the surface of a liquid. The density of liquid is greater than that of soild. The tension in the string is $T_o$. When the system is at rest. What will be the tension in the string if the system has upward acceleration 'a'?

Answer 1

Let m be the mass of block. Initially, the block is in equilibrium and F is the up thrust on the block

$F=T_0+mg........\left(1\right)$

The lift is accelerated upwards so g becomes (g + a)

Using Newton’s second law:

$F^{\prime }-T-mg=ma........\left(2\right)$

From the figure, $F^{\prime }=F\left(\frac{g+a}{g}\right)..........\left(3\right)$

Solving equations (1),(2) and (3)

$T=T_0(1+\frac{a}{g})$