Question

The tension in a string holding a solid block below the surface of a liquid (where ${\rho }_{liquid}>{\rho }_{block}$) as in shown in the figure is $T$ when the system is at rest.Then what will be the tension in the string if the system has upward acceleration $a$?

• A. $T(1-\frac{a}{g})$
• B. $T(1+\frac{a}{g})$
• C. $T(\frac{a}{g}-1)$
• D. $\frac{a}{g}T$

Answer 1

The correct option is B $T(1+\frac{a}{g})$

Initially,

$F_b=T+mg$

$T=\rho \gamma g-Mg=(\rho \gamma -m)g$

When acceleration a is applied

$F^{\prime }b=T^{\prime }+M(g+a)$

$T^{\prime }=(\rho \gamma -M)(g+a)$

$\frac{T^{\prime }}{T}=\left(\frac{g+a}{g}\right)\Rightarrow T^{\prime }=T(1+\frac{a}{g})$