Embibe Experts Solutions for Chapter: Properties of Solid and Liquid, Exercise 1: Exercise 1

Two glasses with identical volumes are filled with water to the half-way mark and are kept side by side. Two solid cubes made of the same metal are now dropped into the two glasses and both of them sink in the water. The first glass is completely filled now. The second glass is still ${\frac{7}{16}}^{\mathrm{th}}$ empty. The ratio of the surface areas of the cubes dropped into the first and the second glass is

A vessel contains oil (density $0.8 \mathrm{g} {\mathrm{cm}}^{-3}$) over mercury (density $13.6 \mathrm{g} {\mathrm{cm}}^{-3}$). A homogeneous sphere floats with half volume immersed in mercury and the other half in oil. What will be the density (in $\mathrm{g} {\mathrm{cm}}^{-3}$) of the material of the sphere?

A metallic spherical ball of mass $M$ is dropped into a liquid and after some time it reaches a terminal velocity of $v$. If another spherical ball of mass $8M$ made of the same metal is dropped into the same liquid, then its terminal velocity will be (assume the spheres to be uniformly dense)

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Let $T$ represent the true weight of a body, $B$ the force of buoyancy on the body when immersed in a liquid, $A$ represents the apparent weight of the body and $W$ be twice the weight of liquid displaced by the body. Then which of the following relation is correct?

A small iron ball falls from rest through a large height $h$ into a water column, the final velocity

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A massless metal plate is placed on a horizontal tabletop lubricated with oil. The sheet is a square of side length $\ell =1.0 \mathrm{m}$ and the oil layer has thickness $\mathrm{h}=1.0 \mathrm{mm}$. Initially one edge of the sheet coincides with one edge of the table. The sheet is pulled outwards without rotation with a constant force $\mathrm{F}=15 \mathrm{N}$. If coefficient of viscosity of the oil is $\eta =0.2 \mathrm{N}-\mathrm{s}/{\mathrm{m}}^2$, how long (in second) will it take to pull half of the sheet out of the table?