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:

The reading of a 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 submerged in water. The specific gravity of the block must be therefore ............

$A$ cubical block of wood of edge $10$ $cm$ and mass $0.92$ $kg$ floats in a tank of water with a layer of oil of relative density $0.6$ to a depth of $4$ $cm$ above the water. When the block attains equilibrium with four of its side edges vertical,which of the following is true?

$A$ solid sphere of radius $R$ and density $\rho$ is attached to one end of a massless spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3\rho$. The complete arrangement is placed in a liquid of density $2\rho$ and is allowed to reach equilibrium. The correct statement$(s)$ is (are):
$(A)$ The net elongation of the spring is $\frac{4 \pi R^3 \rho g}{3 k}$
$(B)$ The net elongation of the spring is $\frac{8 \pi R^3 \rho g}{3 k}$
$(C)$ The light sphere is partially submerged.
$(D)$ The light sphere is completely submerged.

$A$ 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:

$A$ homogeneous solid cylinder of length $L$ $(L < H/2)$ and cross-sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the figure. The lower density liquid is open to the atmosphere having pressure $P_0$. Then,the density $D$ of the solid is given by: