A boat having a length of $3\,metre$ and breadth $2\,metre$ is floating on a lake. The boat sinks by one cm when a man gets on it. Mass of the man is ....... $kg$
$60$
$62$
$72$
$128$
A tall tank filled with water has an irregular shape as shown. The wall $C D$ makes an angle of $45^{\circ}$ with the horizontal, the wall $A B$ is normal to the base $B C$. The lengths $A B$ and $C D$ are much smaller than the height $h$ of water (figure not to scale). Let $p_1, p_2$ and $p_3$ be the pressures exerted by the water on the wall $A B$, base $B C$ and the wall $C D$ respectively. Density of water is $\rho$ and $g$ is acceleration due to gravity. Then, approximately
A dumbbell is placed in water of density $\rho$ . It is observed that by attaching a mass $m$ to the rod, the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass $m$ is negligible. The value of length $l$ is
Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged if the density of ice is ${\rho _i} = 0.917\,g/c{m^3}$.
A sample of metal weighs $210 gm$ in air, $180 gm$ in water and $120 gm$ in liquid. Then relative density $(RD) $ of
The reading of spring balance when a block is suspended from it in air, is $60\,N$. This reading is changed to $40\, N$ when the block is immersed in water. The specific density of the block is