Question

A string is holding a soild block below the surface of a liquid. The density of liquid is greater then that of solid. The tension in the string is $T_0$. When the system is at rest. What will be the tension in the string if the system has upward acceleration a?

• A. $T_0[1+\frac{a}{g}]$
• B. $T_0[1+\frac{2a}{g}]$
• C. $T_0[1-\frac{g}{a}]$
• D. $T_0[1+\frac{g}{a}]$

Answer 1

The correct option is A $T_0[1+\frac{a}{g}]$

Let $m$ be the mass of block$.$

Initially for the equilibrium of block$.$

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

here$,$ $F$ is the upthrust on the block

when the lift is accelerated upwards$,$ $g_{eff}$ becomes $g+a$ instead of $g.$

hence,

$F^{\prime }=F\left(\frac{g+a}{g}\right)$------------------$\left(2\right)$

From newton's second law

$F^{\prime }-T-mg=ma$----------------------$\left(3\right)$

Solving $e{q}^n\left(1\right),\left(2\right)and\left(3\right),$ we get

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

Hence,

option $\left(A\right)$ is correct answer.