A piece of gold weighs $10 \,g$ in air and $9 \,g$ in water. What is the volume of cavity is ...... $cc$ (Density of gold $=19.3 \,g cm ^{-3}$ )
$0.182$
$0.282$
$0.382$
$0.482$
$Assertion :$ A thin stainless steel needle can lay floating on a still water surface.
$Reason :$ Any object floats when the buoyancy force balances the weight of the object
The spring balance $A$ reads $2\, kg$ with a block m suspended from it. $A $ balance $B$ reads $5 \,kg $ when a beaker filled with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid as shown in figure. In this situation
A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If $\rho_0$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is
A rectangular box has water in it. It is being pulled to the right with an acceleration $a$. Which of the following options shows the correct shape of water surface on it ?
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