A block of ice floats on a liquid of density | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $M$ be the mass of the ice block.According to the principle of floatation,the weight of the ice equals the weight of the liquid displaced.Thus

Vedclass · Accepted Answer

Rises

Vedclass · Answer

(B) Let $M$ be the mass of the ice block.According to the principle of floatation,the weight of the ice equals the weight of the liquid displaced.Thus,$M \cdot g = V_D \cdot \sigma_L \cdot g$,where $V_D$ is the volume of liquid displaced and $\sigma_L$ is the density of the liquid.Therefore,$V_D = \frac{M}{\sigma_L}$.When the ice melts,it forms water of mass $M$. The volume of this water is $V_F = \frac{M}{\sigma_W}$,where $\sigma_W$ is the density of water $(1 \ g/cm^3)$.Given $\sigma_L = 1.2 \ g/cm^3$ and $\sigma_W = 1 \ g/cm^3$,we have $\sigma_L > \sigma_W$.Comparing the volumes: Since $\sigma_L > \sigma_W$,it follows that $\frac{M}{\sigma_L} Since the volume of the water formed $(V_F)$ is greater than the volume of the liquid displaced by the floating ice $(V_D)$,the level of the liquid in the beaker will rise.

$A$ block of ice floats on a liquid of density $1.2 \ g/cm^3$ in a beaker. What happens to the level of the liquid when the ice completely melts?

Similar Questions

$A$ 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:

$A$ sample of metal weighs $210 \ g$ in air,$180 \ g$ in water,and $120 \ g$ in a liquid. Then,the relative density $(RD)$ of:

$A$ metal ball of density $7800 \ kg/m^3$ is suspected to have a large number of cavities. It weighs $9.8 \ kg$ when weighed in air and $1.5 \ kg$ less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately ....... $\%$

$A$ body floats in a liquid contained in a beaker. The whole system falls freely under gravity. The upthrust on the body due to the liquid is

$A$ container of large surface area is filled with a liquid of density $\rho$. $A$ cubical block of side edge $a$ and mass $M$ is floating in it with four-fifths of its volume submerged. If a coin of mass $m$ is placed gently on the top surface of the block,it is just submerged. $M$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module