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# A solid blocks whose density is greater then the density of liquid is placed inside the liquid. It begins to float. Now a string attached to the solid holds the solid submerged. Now the tension in the string is $T_1$. If the system is accelerated upward with an acceleration a how will the tension in the string change.

a) increase

b) remain same

c) depends on the density of liquid.

d) depends on the height of liquid column.

Free body diagram
Case 1 -
When the system is at rest
Where F=upthrust
$F= T_0+mg$
Case 2 -
We know that when the $F'-T'-mg=ma$
We know that when a body is accelerated upwards with acceleration a. effective acceleration is $(g+a)$
$\therefore F'=F \bigg(\large\frac{g+a}{g}\bigg)$ --------(1)
$F \bigg(\large\frac{g+a}{g}\bigg)$$-T=m (g+a) --------(2) (T_0+mg)\bigg(\large\frac{g+a}{g}\bigg)$$-m(g+a)=T^1$
$T_0 \bigg(\large\frac{g+a}{g}\bigg)$$+m(g+a)-m(g+a)=T^1$
$T'= T_0 \large\frac{(g+a)}{g}$
$\therefore$ Tension in the string increases
Hence a is the correct answer

edited Feb 18, 2014 by meena.p