A hollow sphere of mass $M$ and radius $r$ is immersed in a tank of water (density $\rho$$_w$ ). The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which makes angle $45^o$ with the horizontal as shown in the figure. The tension $T_1$ in the wire is :
$\frac{{\frac{4}{3}\pi \,{R^3}{\rho _w}g - Mg}}{{\sqrt 2 }}$
$\frac{2}{3}\pi \,{R^3}{\rho _w}g - Mg$
$\frac{{\frac{4}{3}\pi \,{R^3}{\rho _w}g - Mg}}{2}$
$\frac{4}{3}\pi \,{R^3}{\rho _w}g + Mg$
A pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. A container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it’s balanced. A brass weight on the end of a string is then lowered into the water, but not allowed to rest on the bottom of the container. What happens next ?
A metallic sphere weighing $3 \,kg$ in air is held by a string so as to be completely immersed in a liquid of relative density $0.8$. The relative density of metallic is $10$. The tension in the string is ........ $N$
A sample of metal weighs $210 gm$ in air, $180 gm$ in water and $120 gm$ in liquid. Then relative density $(RD) $ of
If $W$ be the weight of a body of density $\rho $ in vacuum then its apparent weight in air of density $\sigma $ is
A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid. If whole of the system accelerates upward with acceleration $g / 4$, the fraction of volume immersed in the liquid will be ..........