Question

A brass sphere weighs $100gm.wt$ in air. It is suspended by a thread in a liquid of specific gravity $=0.8$. If the specific gravity of brass is $8$, the tension in the thread in newtons is :

• A. $0.0882$
• B. $8.82$
• C. $0.882$
• D. $0.00882$

Answer 1

The correct option is C $0.882$

Given,

$m=100gm=0.1kg$ mass of brass

$d_l=0.8$, density of liquid

$d_b=8$

$g=9.8m/s^2$

From the free body diagram,

$mg=T+F_b$. . . .(1)

Lets consider

$V=$ volume of liquid

$d_l=\frac{m}{V}$

and $F_b=V{d}_{l}g$ thrust in liquid

from equation (1)

$mg=T+V{d}_{l}g$

$T=mg-V{d}_{l}g=mg-\frac{V{d}_b}{d_b}{d}_{l}g$

$T=mg(1-\frac{d_l}{d_b})$

$T=0.1\times 9.8(1-\frac{0.8}{8})$

$T=0.882N$

The correct option is C.