07. Law of Floating Bodies
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Mechanical Properties of Fluids

143326 A motor boat of mass $m$ moves along a lake with velocity $v_{0}$. Assume that resistance of water is proportional to velocity of boat as $\overrightarrow{\mathbf{F}}=-\mathbf{r}, \mathbf{v}$ being the proportionality constant. At the moment $t=0$, the engine of the boat is shut down.
The instantaneous velocity as a function of time $t$ is proportional to

1 $\frac{\mathrm{rt}}{\mathrm{e}^{\mathrm{m}}}$
2 $e^{-\frac{r t}{m}}$
3 $\operatorname{In}\left(\frac{\mathrm{rt}}{\mathrm{m}}\right)$
4 $\operatorname{In}\left(\frac{\mathrm{ml}}{\mathrm{r}}\right)$
SCRA-2015
Mechanical Properties of Fluids

143327 A motor boat of mass $m$ moves along a lake with velocity $v_{0}$. Assume that resistance of water is proportional to velocity of boat as $\overrightarrow{\mathbf{F}}=-\mathbf{r}, \mathbf{r}$ being the proportionality constant. At the moment $t=0$, the engine of the boat is shut down.
The total distance covered till it stops is

1 $\frac{\mathrm{mv}_{0}}{\mathrm{r}}$
2 $\frac{\mathrm{mv}_{0}}{2 \mathrm{r}}$
3 $\frac{\mathrm{mv}_{0}}{4 \mathrm{r}}$
4 $\frac{2 \mathrm{mv}_{0}}{\mathrm{r}}$
SCRA-2015
Mechanical Properties of Fluids

143328 A sphere of relative density $\rho$ and diameter $D$ has concentric cavity of diameter $d$. When the sphere just floats on water in a tank, then which one of the following is correct?

1 $\frac{\mathrm{D}}{\mathrm{d}}=\left(\frac{\rho+1}{\rho}\right)^{1 / 3}$
2 $\frac{\mathrm{D}}{\mathrm{d}}=\left(\frac{\rho-1}{\rho}\right)^{1 / 3}$
3 $\frac{D}{d}=\left(\frac{\rho}{\rho-1}\right)^{1 / 3}$
4 $\frac{\mathrm{D}}{d}=\left(\frac{\rho}{\rho+1}\right)^{1 / 3}$
SCRA-2014
Mechanical Properties of Fluids

143329 A piece of cork floats in a vessel filled with kerosene. What part of its volume is submerged in kerosene?
[density of cork $=200 \mathrm{~kg} / \mathrm{m}^{3}$ and density of kerosene $=800 \mathrm{~kg} / \mathrm{m}^{3}$ ]

1 $\frac{1}{5}$
2 $\frac{1}{4}$
3 $\frac{1}{3}$
4 $\frac{3}{4}$
SCRA-2014
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Mechanical Properties of Fluids

143326 A motor boat of mass $m$ moves along a lake with velocity $v_{0}$. Assume that resistance of water is proportional to velocity of boat as $\overrightarrow{\mathbf{F}}=-\mathbf{r}, \mathbf{v}$ being the proportionality constant. At the moment $t=0$, the engine of the boat is shut down.
The instantaneous velocity as a function of time $t$ is proportional to

1 $\frac{\mathrm{rt}}{\mathrm{e}^{\mathrm{m}}}$
2 $e^{-\frac{r t}{m}}$
3 $\operatorname{In}\left(\frac{\mathrm{rt}}{\mathrm{m}}\right)$
4 $\operatorname{In}\left(\frac{\mathrm{ml}}{\mathrm{r}}\right)$
SCRA-2015
Mechanical Properties of Fluids

143327 A motor boat of mass $m$ moves along a lake with velocity $v_{0}$. Assume that resistance of water is proportional to velocity of boat as $\overrightarrow{\mathbf{F}}=-\mathbf{r}, \mathbf{r}$ being the proportionality constant. At the moment $t=0$, the engine of the boat is shut down.
The total distance covered till it stops is

1 $\frac{\mathrm{mv}_{0}}{\mathrm{r}}$
2 $\frac{\mathrm{mv}_{0}}{2 \mathrm{r}}$
3 $\frac{\mathrm{mv}_{0}}{4 \mathrm{r}}$
4 $\frac{2 \mathrm{mv}_{0}}{\mathrm{r}}$
SCRA-2015
Mechanical Properties of Fluids

143328 A sphere of relative density $\rho$ and diameter $D$ has concentric cavity of diameter $d$. When the sphere just floats on water in a tank, then which one of the following is correct?

1 $\frac{\mathrm{D}}{\mathrm{d}}=\left(\frac{\rho+1}{\rho}\right)^{1 / 3}$
2 $\frac{\mathrm{D}}{\mathrm{d}}=\left(\frac{\rho-1}{\rho}\right)^{1 / 3}$
3 $\frac{D}{d}=\left(\frac{\rho}{\rho-1}\right)^{1 / 3}$
4 $\frac{\mathrm{D}}{d}=\left(\frac{\rho}{\rho+1}\right)^{1 / 3}$
SCRA-2014
Mechanical Properties of Fluids

143329 A piece of cork floats in a vessel filled with kerosene. What part of its volume is submerged in kerosene?
[density of cork $=200 \mathrm{~kg} / \mathrm{m}^{3}$ and density of kerosene $=800 \mathrm{~kg} / \mathrm{m}^{3}$ ]

1 $\frac{1}{5}$
2 $\frac{1}{4}$
3 $\frac{1}{3}$
4 $\frac{3}{4}$
SCRA-2014
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Mechanical Properties of Fluids

143326 A motor boat of mass $m$ moves along a lake with velocity $v_{0}$. Assume that resistance of water is proportional to velocity of boat as $\overrightarrow{\mathbf{F}}=-\mathbf{r}, \mathbf{v}$ being the proportionality constant. At the moment $t=0$, the engine of the boat is shut down.
The instantaneous velocity as a function of time $t$ is proportional to

1 $\frac{\mathrm{rt}}{\mathrm{e}^{\mathrm{m}}}$
2 $e^{-\frac{r t}{m}}$
3 $\operatorname{In}\left(\frac{\mathrm{rt}}{\mathrm{m}}\right)$
4 $\operatorname{In}\left(\frac{\mathrm{ml}}{\mathrm{r}}\right)$
SCRA-2015
Mechanical Properties of Fluids

143327 A motor boat of mass $m$ moves along a lake with velocity $v_{0}$. Assume that resistance of water is proportional to velocity of boat as $\overrightarrow{\mathbf{F}}=-\mathbf{r}, \mathbf{r}$ being the proportionality constant. At the moment $t=0$, the engine of the boat is shut down.
The total distance covered till it stops is

1 $\frac{\mathrm{mv}_{0}}{\mathrm{r}}$
2 $\frac{\mathrm{mv}_{0}}{2 \mathrm{r}}$
3 $\frac{\mathrm{mv}_{0}}{4 \mathrm{r}}$
4 $\frac{2 \mathrm{mv}_{0}}{\mathrm{r}}$
SCRA-2015
Mechanical Properties of Fluids

143328 A sphere of relative density $\rho$ and diameter $D$ has concentric cavity of diameter $d$. When the sphere just floats on water in a tank, then which one of the following is correct?

1 $\frac{\mathrm{D}}{\mathrm{d}}=\left(\frac{\rho+1}{\rho}\right)^{1 / 3}$
2 $\frac{\mathrm{D}}{\mathrm{d}}=\left(\frac{\rho-1}{\rho}\right)^{1 / 3}$
3 $\frac{D}{d}=\left(\frac{\rho}{\rho-1}\right)^{1 / 3}$
4 $\frac{\mathrm{D}}{d}=\left(\frac{\rho}{\rho+1}\right)^{1 / 3}$
SCRA-2014
Mechanical Properties of Fluids

143329 A piece of cork floats in a vessel filled with kerosene. What part of its volume is submerged in kerosene?
[density of cork $=200 \mathrm{~kg} / \mathrm{m}^{3}$ and density of kerosene $=800 \mathrm{~kg} / \mathrm{m}^{3}$ ]

1 $\frac{1}{5}$
2 $\frac{1}{4}$
3 $\frac{1}{3}$
4 $\frac{3}{4}$
SCRA-2014
For More Updates join with Us
Mechanical Properties of Fluids

143326 A motor boat of mass $m$ moves along a lake with velocity $v_{0}$. Assume that resistance of water is proportional to velocity of boat as $\overrightarrow{\mathbf{F}}=-\mathbf{r}, \mathbf{v}$ being the proportionality constant. At the moment $t=0$, the engine of the boat is shut down.
The instantaneous velocity as a function of time $t$ is proportional to

1 $\frac{\mathrm{rt}}{\mathrm{e}^{\mathrm{m}}}$
2 $e^{-\frac{r t}{m}}$
3 $\operatorname{In}\left(\frac{\mathrm{rt}}{\mathrm{m}}\right)$
4 $\operatorname{In}\left(\frac{\mathrm{ml}}{\mathrm{r}}\right)$
SCRA-2015
Mechanical Properties of Fluids

143327 A motor boat of mass $m$ moves along a lake with velocity $v_{0}$. Assume that resistance of water is proportional to velocity of boat as $\overrightarrow{\mathbf{F}}=-\mathbf{r}, \mathbf{r}$ being the proportionality constant. At the moment $t=0$, the engine of the boat is shut down.
The total distance covered till it stops is

1 $\frac{\mathrm{mv}_{0}}{\mathrm{r}}$
2 $\frac{\mathrm{mv}_{0}}{2 \mathrm{r}}$
3 $\frac{\mathrm{mv}_{0}}{4 \mathrm{r}}$
4 $\frac{2 \mathrm{mv}_{0}}{\mathrm{r}}$
SCRA-2015
Mechanical Properties of Fluids

143328 A sphere of relative density $\rho$ and diameter $D$ has concentric cavity of diameter $d$. When the sphere just floats on water in a tank, then which one of the following is correct?

1 $\frac{\mathrm{D}}{\mathrm{d}}=\left(\frac{\rho+1}{\rho}\right)^{1 / 3}$
2 $\frac{\mathrm{D}}{\mathrm{d}}=\left(\frac{\rho-1}{\rho}\right)^{1 / 3}$
3 $\frac{D}{d}=\left(\frac{\rho}{\rho-1}\right)^{1 / 3}$
4 $\frac{\mathrm{D}}{d}=\left(\frac{\rho}{\rho+1}\right)^{1 / 3}$
SCRA-2014
Mechanical Properties of Fluids

143329 A piece of cork floats in a vessel filled with kerosene. What part of its volume is submerged in kerosene?
[density of cork $=200 \mathrm{~kg} / \mathrm{m}^{3}$ and density of kerosene $=800 \mathrm{~kg} / \mathrm{m}^{3}$ ]

1 $\frac{1}{5}$
2 $\frac{1}{4}$
3 $\frac{1}{3}$
4 $\frac{3}{4}$
SCRA-2014