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 vessel containing water is given a constant acceleration a towards the right, along a straight horizontal path. Which of the following diagram represents the surface of the liquid
Two cubical blocks identical in dimensions float in water in such a way that $1$ st block floats with half part immersed in water and second block floats with $3 / 4$ of its volume inside the water. The ratio of densities of blocks is ..........
A stream-lined body falls through air from a height $h$ on the surface of liquid. Let $d$ and $D$ denote the densities of the materials of the body and the liquid respectively. If $D > d$, then the time after which the body will be instantaneously at rest, is
Two non-mixing liquids of densities $\rho $ and $n \rho \,(n > 1)$ are put in a container. The height of each liquid is $h.$ A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $\rho L (\rho < 1)$ in the denser liquid. The density $d$ is equal to
A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body