143242
To what height water should be filled in a container of height $21 \mathrm{~cm}$, so that it appears as half filled when viewed from the top $\left(\right.$ Take $\left._{\mathrm{a}} \mu_{\mathrm{w}}=\frac{4}{3}\right)$
1 $12 \mathrm{~cm}$
2 $15 \mathrm{~cm}$
3 $10.5 \mathrm{~cm}$
4 $7 \mathrm{~cm}$
Explanation:
A Given, ${ }_{\mathrm{a}} \mu_{\mathrm{w}}=\frac{4}{3}$ Apparent depth $h^{\prime}=(21-x)$ Real depth $\mathrm{h}=\mathrm{x}$ refractive index of water $=\frac{\text { Real depth }}{\text { Apparent depth }}$ $\therefore \quad \mu =\frac{\mathrm{h}}{\mathrm{h}^{\prime}}$ $\frac{4}{3} =\frac{\mathrm{x}}{21-\mathrm{x}}$ $\mathrm{x} =12 \mathrm{~cm}$
BCECE-2012
Mechanical Properties of Fluids
143243
A wooden ball of density $\rho$ is immersed in a liquid of density $\sigma$ to a depth $h$ below the surface of water and then released. The height to which the ball jumps out of water is:
1 $\left(1-\frac{\rho}{\sigma}\right) \mathrm{h}$
2 $\left(1+\frac{\rho}{\sigma}\right) \mathrm{h}$
3 $\left(\frac{\rho}{\sigma}-1\right) \mathrm{h}$
4 $\left(\frac{\sigma}{\rho}-1\right) \mathrm{h}$
Explanation:
D Weight of the ball $=\mathrm{V} \rho \mathrm{g}$ upward thrust on ball $=\mathrm{V} \sigma \mathrm{g}-\mathrm{V} \rho \mathrm{g}$ Upward acceleration $(\mathrm{a})=\frac{\mathrm{V} \sigma \mathrm{g}-\mathrm{V} \rho \mathrm{g}}{\mathrm{V} \rho}=\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{g}$ $\because \quad \mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{as}=2$ as $\quad[\because \mathrm{u}=0]$ $\mathrm{v}^{2}=2 \times\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{gh}$ For the motion of the ball outside the water, $\text { K.E. }=\text { P.E. at height } \mathrm{H}$ $\frac{1}{2} \mathrm{mv}^{2}=\mathrm{mgH}$ $\mathrm{H}=\frac{\mathrm{v}^{2}}{2 \mathrm{~g}}=\frac{2 \mathrm{gh}(\sigma-\rho) / \rho}{2 \mathrm{~g}}$ $\mathrm{H}=\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{h}=\left(\frac{\sigma}{\rho}-1\right) \mathrm{h}$
SCRA-2012
Mechanical Properties of Fluids
143244
A sphere of solid material of specific gravity 8 has a concentric spherical cavity and just sinks in water. What should be the ratio of radius of the cavity to that of outer radius of sphere?
1 $\frac{\sqrt[3]{3}}{2}$
2 $\frac{\sqrt[3]{5}}{2}$
3 $\frac{\sqrt[3]{7}}{2}$
4 $\frac{\sqrt[3]{9}}{2}$
Explanation:
C Weight of sphere $=$ Weight of water displaced $\mathrm{W}_{\mathrm{S}}=\mathrm{W}_{\mathrm{w}}$ $\mathrm{V}_{\mathrm{s}} \times \rho_{\mathrm{s}} \times \mathrm{g}=\mathrm{V}_{\mathrm{w}} \times \rho_{\mathrm{w}} \times \mathrm{g}$ Here, $\rho_{\mathrm{s}}=8 \rho_{\mathrm{w}}$ $\frac{4}{3} \pi\left(R^{3}-r^{3}\right) \rho_{s} \times g=\frac{4}{3} \pi R^{3} \times \rho_{w} g$ $8\left(\mathrm{R}^{3}-\mathrm{r}^{3}\right)=\mathrm{R}^{3}$ $\frac{\mathrm{r}^{3}}{\mathrm{R}^{3}}=\frac{7}{8}$ $\frac{\mathrm{r}}{\mathrm{R}}=\frac{\sqrt[3]{7}}{2}$
SCRA-2010
Mechanical Properties of Fluids
143245
An ideal fluid flows through a pipe of circular cross-section with diameters $5 \mathrm{~cm}$ and $10 \mathrm{~cm}$ as shown in the figure. The ratio of velocities of fluid at $A$ and $B$ is :
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Mechanical Properties of Fluids
143242
To what height water should be filled in a container of height $21 \mathrm{~cm}$, so that it appears as half filled when viewed from the top $\left(\right.$ Take $\left._{\mathrm{a}} \mu_{\mathrm{w}}=\frac{4}{3}\right)$
1 $12 \mathrm{~cm}$
2 $15 \mathrm{~cm}$
3 $10.5 \mathrm{~cm}$
4 $7 \mathrm{~cm}$
Explanation:
A Given, ${ }_{\mathrm{a}} \mu_{\mathrm{w}}=\frac{4}{3}$ Apparent depth $h^{\prime}=(21-x)$ Real depth $\mathrm{h}=\mathrm{x}$ refractive index of water $=\frac{\text { Real depth }}{\text { Apparent depth }}$ $\therefore \quad \mu =\frac{\mathrm{h}}{\mathrm{h}^{\prime}}$ $\frac{4}{3} =\frac{\mathrm{x}}{21-\mathrm{x}}$ $\mathrm{x} =12 \mathrm{~cm}$
BCECE-2012
Mechanical Properties of Fluids
143243
A wooden ball of density $\rho$ is immersed in a liquid of density $\sigma$ to a depth $h$ below the surface of water and then released. The height to which the ball jumps out of water is:
1 $\left(1-\frac{\rho}{\sigma}\right) \mathrm{h}$
2 $\left(1+\frac{\rho}{\sigma}\right) \mathrm{h}$
3 $\left(\frac{\rho}{\sigma}-1\right) \mathrm{h}$
4 $\left(\frac{\sigma}{\rho}-1\right) \mathrm{h}$
Explanation:
D Weight of the ball $=\mathrm{V} \rho \mathrm{g}$ upward thrust on ball $=\mathrm{V} \sigma \mathrm{g}-\mathrm{V} \rho \mathrm{g}$ Upward acceleration $(\mathrm{a})=\frac{\mathrm{V} \sigma \mathrm{g}-\mathrm{V} \rho \mathrm{g}}{\mathrm{V} \rho}=\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{g}$ $\because \quad \mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{as}=2$ as $\quad[\because \mathrm{u}=0]$ $\mathrm{v}^{2}=2 \times\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{gh}$ For the motion of the ball outside the water, $\text { K.E. }=\text { P.E. at height } \mathrm{H}$ $\frac{1}{2} \mathrm{mv}^{2}=\mathrm{mgH}$ $\mathrm{H}=\frac{\mathrm{v}^{2}}{2 \mathrm{~g}}=\frac{2 \mathrm{gh}(\sigma-\rho) / \rho}{2 \mathrm{~g}}$ $\mathrm{H}=\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{h}=\left(\frac{\sigma}{\rho}-1\right) \mathrm{h}$
SCRA-2012
Mechanical Properties of Fluids
143244
A sphere of solid material of specific gravity 8 has a concentric spherical cavity and just sinks in water. What should be the ratio of radius of the cavity to that of outer radius of sphere?
1 $\frac{\sqrt[3]{3}}{2}$
2 $\frac{\sqrt[3]{5}}{2}$
3 $\frac{\sqrt[3]{7}}{2}$
4 $\frac{\sqrt[3]{9}}{2}$
Explanation:
C Weight of sphere $=$ Weight of water displaced $\mathrm{W}_{\mathrm{S}}=\mathrm{W}_{\mathrm{w}}$ $\mathrm{V}_{\mathrm{s}} \times \rho_{\mathrm{s}} \times \mathrm{g}=\mathrm{V}_{\mathrm{w}} \times \rho_{\mathrm{w}} \times \mathrm{g}$ Here, $\rho_{\mathrm{s}}=8 \rho_{\mathrm{w}}$ $\frac{4}{3} \pi\left(R^{3}-r^{3}\right) \rho_{s} \times g=\frac{4}{3} \pi R^{3} \times \rho_{w} g$ $8\left(\mathrm{R}^{3}-\mathrm{r}^{3}\right)=\mathrm{R}^{3}$ $\frac{\mathrm{r}^{3}}{\mathrm{R}^{3}}=\frac{7}{8}$ $\frac{\mathrm{r}}{\mathrm{R}}=\frac{\sqrt[3]{7}}{2}$
SCRA-2010
Mechanical Properties of Fluids
143245
An ideal fluid flows through a pipe of circular cross-section with diameters $5 \mathrm{~cm}$ and $10 \mathrm{~cm}$ as shown in the figure. The ratio of velocities of fluid at $A$ and $B$ is :
143242
To what height water should be filled in a container of height $21 \mathrm{~cm}$, so that it appears as half filled when viewed from the top $\left(\right.$ Take $\left._{\mathrm{a}} \mu_{\mathrm{w}}=\frac{4}{3}\right)$
1 $12 \mathrm{~cm}$
2 $15 \mathrm{~cm}$
3 $10.5 \mathrm{~cm}$
4 $7 \mathrm{~cm}$
Explanation:
A Given, ${ }_{\mathrm{a}} \mu_{\mathrm{w}}=\frac{4}{3}$ Apparent depth $h^{\prime}=(21-x)$ Real depth $\mathrm{h}=\mathrm{x}$ refractive index of water $=\frac{\text { Real depth }}{\text { Apparent depth }}$ $\therefore \quad \mu =\frac{\mathrm{h}}{\mathrm{h}^{\prime}}$ $\frac{4}{3} =\frac{\mathrm{x}}{21-\mathrm{x}}$ $\mathrm{x} =12 \mathrm{~cm}$
BCECE-2012
Mechanical Properties of Fluids
143243
A wooden ball of density $\rho$ is immersed in a liquid of density $\sigma$ to a depth $h$ below the surface of water and then released. The height to which the ball jumps out of water is:
1 $\left(1-\frac{\rho}{\sigma}\right) \mathrm{h}$
2 $\left(1+\frac{\rho}{\sigma}\right) \mathrm{h}$
3 $\left(\frac{\rho}{\sigma}-1\right) \mathrm{h}$
4 $\left(\frac{\sigma}{\rho}-1\right) \mathrm{h}$
Explanation:
D Weight of the ball $=\mathrm{V} \rho \mathrm{g}$ upward thrust on ball $=\mathrm{V} \sigma \mathrm{g}-\mathrm{V} \rho \mathrm{g}$ Upward acceleration $(\mathrm{a})=\frac{\mathrm{V} \sigma \mathrm{g}-\mathrm{V} \rho \mathrm{g}}{\mathrm{V} \rho}=\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{g}$ $\because \quad \mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{as}=2$ as $\quad[\because \mathrm{u}=0]$ $\mathrm{v}^{2}=2 \times\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{gh}$ For the motion of the ball outside the water, $\text { K.E. }=\text { P.E. at height } \mathrm{H}$ $\frac{1}{2} \mathrm{mv}^{2}=\mathrm{mgH}$ $\mathrm{H}=\frac{\mathrm{v}^{2}}{2 \mathrm{~g}}=\frac{2 \mathrm{gh}(\sigma-\rho) / \rho}{2 \mathrm{~g}}$ $\mathrm{H}=\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{h}=\left(\frac{\sigma}{\rho}-1\right) \mathrm{h}$
SCRA-2012
Mechanical Properties of Fluids
143244
A sphere of solid material of specific gravity 8 has a concentric spherical cavity and just sinks in water. What should be the ratio of radius of the cavity to that of outer radius of sphere?
1 $\frac{\sqrt[3]{3}}{2}$
2 $\frac{\sqrt[3]{5}}{2}$
3 $\frac{\sqrt[3]{7}}{2}$
4 $\frac{\sqrt[3]{9}}{2}$
Explanation:
C Weight of sphere $=$ Weight of water displaced $\mathrm{W}_{\mathrm{S}}=\mathrm{W}_{\mathrm{w}}$ $\mathrm{V}_{\mathrm{s}} \times \rho_{\mathrm{s}} \times \mathrm{g}=\mathrm{V}_{\mathrm{w}} \times \rho_{\mathrm{w}} \times \mathrm{g}$ Here, $\rho_{\mathrm{s}}=8 \rho_{\mathrm{w}}$ $\frac{4}{3} \pi\left(R^{3}-r^{3}\right) \rho_{s} \times g=\frac{4}{3} \pi R^{3} \times \rho_{w} g$ $8\left(\mathrm{R}^{3}-\mathrm{r}^{3}\right)=\mathrm{R}^{3}$ $\frac{\mathrm{r}^{3}}{\mathrm{R}^{3}}=\frac{7}{8}$ $\frac{\mathrm{r}}{\mathrm{R}}=\frac{\sqrt[3]{7}}{2}$
SCRA-2010
Mechanical Properties of Fluids
143245
An ideal fluid flows through a pipe of circular cross-section with diameters $5 \mathrm{~cm}$ and $10 \mathrm{~cm}$ as shown in the figure. The ratio of velocities of fluid at $A$ and $B$ is :
143242
To what height water should be filled in a container of height $21 \mathrm{~cm}$, so that it appears as half filled when viewed from the top $\left(\right.$ Take $\left._{\mathrm{a}} \mu_{\mathrm{w}}=\frac{4}{3}\right)$
1 $12 \mathrm{~cm}$
2 $15 \mathrm{~cm}$
3 $10.5 \mathrm{~cm}$
4 $7 \mathrm{~cm}$
Explanation:
A Given, ${ }_{\mathrm{a}} \mu_{\mathrm{w}}=\frac{4}{3}$ Apparent depth $h^{\prime}=(21-x)$ Real depth $\mathrm{h}=\mathrm{x}$ refractive index of water $=\frac{\text { Real depth }}{\text { Apparent depth }}$ $\therefore \quad \mu =\frac{\mathrm{h}}{\mathrm{h}^{\prime}}$ $\frac{4}{3} =\frac{\mathrm{x}}{21-\mathrm{x}}$ $\mathrm{x} =12 \mathrm{~cm}$
BCECE-2012
Mechanical Properties of Fluids
143243
A wooden ball of density $\rho$ is immersed in a liquid of density $\sigma$ to a depth $h$ below the surface of water and then released. The height to which the ball jumps out of water is:
1 $\left(1-\frac{\rho}{\sigma}\right) \mathrm{h}$
2 $\left(1+\frac{\rho}{\sigma}\right) \mathrm{h}$
3 $\left(\frac{\rho}{\sigma}-1\right) \mathrm{h}$
4 $\left(\frac{\sigma}{\rho}-1\right) \mathrm{h}$
Explanation:
D Weight of the ball $=\mathrm{V} \rho \mathrm{g}$ upward thrust on ball $=\mathrm{V} \sigma \mathrm{g}-\mathrm{V} \rho \mathrm{g}$ Upward acceleration $(\mathrm{a})=\frac{\mathrm{V} \sigma \mathrm{g}-\mathrm{V} \rho \mathrm{g}}{\mathrm{V} \rho}=\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{g}$ $\because \quad \mathrm{v}^{2}=\mathrm{u}^{2}+2 \mathrm{as}=2$ as $\quad[\because \mathrm{u}=0]$ $\mathrm{v}^{2}=2 \times\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{gh}$ For the motion of the ball outside the water, $\text { K.E. }=\text { P.E. at height } \mathrm{H}$ $\frac{1}{2} \mathrm{mv}^{2}=\mathrm{mgH}$ $\mathrm{H}=\frac{\mathrm{v}^{2}}{2 \mathrm{~g}}=\frac{2 \mathrm{gh}(\sigma-\rho) / \rho}{2 \mathrm{~g}}$ $\mathrm{H}=\left(\frac{\sigma-\rho}{\rho}\right) \mathrm{h}=\left(\frac{\sigma}{\rho}-1\right) \mathrm{h}$
SCRA-2012
Mechanical Properties of Fluids
143244
A sphere of solid material of specific gravity 8 has a concentric spherical cavity and just sinks in water. What should be the ratio of radius of the cavity to that of outer radius of sphere?
1 $\frac{\sqrt[3]{3}}{2}$
2 $\frac{\sqrt[3]{5}}{2}$
3 $\frac{\sqrt[3]{7}}{2}$
4 $\frac{\sqrt[3]{9}}{2}$
Explanation:
C Weight of sphere $=$ Weight of water displaced $\mathrm{W}_{\mathrm{S}}=\mathrm{W}_{\mathrm{w}}$ $\mathrm{V}_{\mathrm{s}} \times \rho_{\mathrm{s}} \times \mathrm{g}=\mathrm{V}_{\mathrm{w}} \times \rho_{\mathrm{w}} \times \mathrm{g}$ Here, $\rho_{\mathrm{s}}=8 \rho_{\mathrm{w}}$ $\frac{4}{3} \pi\left(R^{3}-r^{3}\right) \rho_{s} \times g=\frac{4}{3} \pi R^{3} \times \rho_{w} g$ $8\left(\mathrm{R}^{3}-\mathrm{r}^{3}\right)=\mathrm{R}^{3}$ $\frac{\mathrm{r}^{3}}{\mathrm{R}^{3}}=\frac{7}{8}$ $\frac{\mathrm{r}}{\mathrm{R}}=\frac{\sqrt[3]{7}}{2}$
SCRA-2010
Mechanical Properties of Fluids
143245
An ideal fluid flows through a pipe of circular cross-section with diameters $5 \mathrm{~cm}$ and $10 \mathrm{~cm}$ as shown in the figure. The ratio of velocities of fluid at $A$ and $B$ is :
