$A$ hollow sphere of external radius $R$ and thickness $t$ $(t \ll R)$ is made of a metal of density $\rho$. The sphere will float in water if:

Two rods of the same material and length have their electric resistance in the ratio $1:2$. When both rods are dipped in water,the correct statement will be:

$Assertion$ : $A$ balloon filled with hydrogen will fall with acceleration $\frac{g}{6}$ on the moon.
$Reason$ : Moon has no atmosphere.

State the law of floatation and describe its cases.

$A$ boy carries a fish in one hand and a bucket (not full) of water in the other hand. If he places the fish in the bucket,the weight now carried by him (assume that water does not spill) is:

$A$ tub is filled with water and a wooden cube $10 \ \text{cm} \times 10 \ \text{cm} \times 10 \ \text{cm}$ is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by $3.87 \ \text{cm}$. The mass of the metal coin is . . . . . . gram. (Take water density as $1 \ \text{g/cm}^3$ and density of wood as $0.4 \ \text{g/cm}^3$)