$A$ cube of side $40 \ cm$ is floating with $\frac{1}{4}$th of its volume immersed in water. When a circular disc is placed on the cube, it floats with $\frac{2}{5}$th of its volume immersed in water. The mass of the disc is (in $kg$)

$A$ spring balance $A$ reads $2 \,kg$ with a block of mass $m$ suspended from it. Another balance $B$ reads $3 \,kg$ when a beaker with a liquid is put on its pan. The two balances are now so arranged that the hanging mass $m$ is fully immersed inside the liquid in the beaker as shown in the figure. In this situation,

$A$ uniform rod is suspended horizontally from its mid-point. $A$ piece of metal whose weight is $w$ is suspended at a distance $l$ from the mid-point. Another weight $w_{1}$ is suspended on the other side at a distance $l_{1}$ from the mid-point to bring the rod to a horizontal position. When $w$ is completely immersed in water, $w_{1}$ needs to be kept at a distance $l_{2}$ from the mid-point to get the rod back into a horizontal position. The specific gravity of the metal piece is

An empty balloon weighs $1\, g$. The balloon is filled with water to the neck and tied with a massless thread. The weight of the balloon along with water is $101\, g$. The balloon filled with water is weighed when fully immersed in water. Its weight in water is ...... $g$.

$A$ wooden block of density $0.5 \ g/cc$ is tied to a string. The other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density $1 \ g/cc$. If the tension of the string is $20 \ N$, then the mass of the block is (Take $g = 10 \ m/s^2$) (in $kg$)

$A$ ball whose density is $0.4 \times 10^3 \, kg/m^3$ falls into water from a height of $9 \, cm$. To what depth does the ball sink? ....... $cm$