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Gravitation

138257 Two spheres of mass $m$ and $M$ are situated in air and the gravitational force between them is 'f. The space around the masses is now filled with of specific gravity 4. The gravitational force will now be

1

4 f

2

f / 4

3

f / 16

4

f

Explanation:

D Let the distance between the two masses be R. Then, $f = \frac{GMm}{R^{2}}$
Since, gravitational force is independent of specific gravity of the surrounding medium.
$∴$ The gravitational force will be $f$ .

BCECE 2013

Gravitation

138258 Two identical solid spheres each of radius $r$ and made up of the material of density $ρ$ are kept in contact with each other. The gravitational force between the two spheres will be proportional to:

1

ρ^{2} r^{4}

2

ρ^{4} r^{2}

3

ρ^{2} r^{3}

4

ρ^{3} r^{2}

Explanation:

A Mass of each sphere $M_{1} = M_{2} = ρ \cdot V = ρ \frac{4 π}{3} r^{3}$ Gravitational force, $F = G \frac{M_{1} M_{2}}{R^{2}}$
$∴$ Sphere are kept in contact each other so that the centre distance is $2 r$
$F = G \frac{ρ^{2} {(\frac{4}{3} π r^{3})}^{2}}{(2 r)^{2}}$
$F = \frac{1}{9} π^{2} ρ^{2} r^{4} G$
So, $F \propto ρ^{2} r^{4}$

MP PET -2013

Gravitation

138262 A point mass $m$ is placed inside a spherical shell of radius $R$ and mass $M$ at a distance $R / 2$ from the centre of the shell. The gravitational force exerted by the shell on the point mass is-

1

\frac{GMm}{R^{2}}

2

- \frac{GMm}{R^{2}}

3 Zero

4

4 \frac{GMm}{R^{2}}

Explanation:

C
If a point mass is placed inside a uniform spherical shell, the gravitational force on the point mass is zero. Hence, the gravitational force exerted by the shell on the point mass is zero.
$E_{Inside} = 0$
$So, F = {mE}_{Inside} = 0$

CG PET-22.05.2022

Gravitation

138267 The weight of a body is $9.8 N$ at the place where $g = 9.8 {ms}^{- 2}$ . Its mass is

1 Zero

2

9.8 kg

3

10 kg

4

1 kg

Explanation:

D $Given,$
$W = 9.8 N, and g = 9.8 m / s^{2}$
$Weight (W) = mg$
$Hence, (m) = \frac{W}{g} = \frac{9.8}{9.8} = 1 kg$

NDA (II) 2009

Gravitation

138257 Two spheres of mass $m$ and $M$ are situated in air and the gravitational force between them is 'f. The space around the masses is now filled with of specific gravity 4. The gravitational force will now be

1

4 f

2

f / 4

3

f / 16

4

f

Explanation:

D Let the distance between the two masses be R. Then, $f = \frac{GMm}{R^{2}}$
Since, gravitational force is independent of specific gravity of the surrounding medium.
$∴$ The gravitational force will be $f$ .

BCECE 2013

Gravitation

138258 Two identical solid spheres each of radius $r$ and made up of the material of density $ρ$ are kept in contact with each other. The gravitational force between the two spheres will be proportional to:

1

ρ^{2} r^{4}

2

ρ^{4} r^{2}

3

ρ^{2} r^{3}

4

ρ^{3} r^{2}

Explanation:

A Mass of each sphere $M_{1} = M_{2} = ρ \cdot V = ρ \frac{4 π}{3} r^{3}$ Gravitational force, $F = G \frac{M_{1} M_{2}}{R^{2}}$
$∴$ Sphere are kept in contact each other so that the centre distance is $2 r$
$F = G \frac{ρ^{2} {(\frac{4}{3} π r^{3})}^{2}}{(2 r)^{2}}$
$F = \frac{1}{9} π^{2} ρ^{2} r^{4} G$
So, $F \propto ρ^{2} r^{4}$

MP PET -2013

Gravitation

138262 A point mass $m$ is placed inside a spherical shell of radius $R$ and mass $M$ at a distance $R / 2$ from the centre of the shell. The gravitational force exerted by the shell on the point mass is-

1

\frac{GMm}{R^{2}}

2

- \frac{GMm}{R^{2}}

3 Zero

4

4 \frac{GMm}{R^{2}}

Explanation:

C
If a point mass is placed inside a uniform spherical shell, the gravitational force on the point mass is zero. Hence, the gravitational force exerted by the shell on the point mass is zero.
$E_{Inside} = 0$
$So, F = {mE}_{Inside} = 0$

CG PET-22.05.2022

Gravitation

138267 The weight of a body is $9.8 N$ at the place where $g = 9.8 {ms}^{- 2}$ . Its mass is

1 Zero

2

9.8 kg

3

10 kg

4

1 kg

Explanation:

D $Given,$
$W = 9.8 N, and g = 9.8 m / s^{2}$
$Weight (W) = mg$
$Hence, (m) = \frac{W}{g} = \frac{9.8}{9.8} = 1 kg$

NDA (II) 2009

Gravitation

138257 Two spheres of mass $m$ and $M$ are situated in air and the gravitational force between them is 'f. The space around the masses is now filled with of specific gravity 4. The gravitational force will now be

1

4 f

2

f / 4

3

f / 16

4

f

Explanation:

D Let the distance between the two masses be R. Then, $f = \frac{GMm}{R^{2}}$
Since, gravitational force is independent of specific gravity of the surrounding medium.
$∴$ The gravitational force will be $f$ .

BCECE 2013

Gravitation

138258 Two identical solid spheres each of radius $r$ and made up of the material of density $ρ$ are kept in contact with each other. The gravitational force between the two spheres will be proportional to:

1

ρ^{2} r^{4}

2

ρ^{4} r^{2}

3

ρ^{2} r^{3}

4

ρ^{3} r^{2}

Explanation:

A Mass of each sphere $M_{1} = M_{2} = ρ \cdot V = ρ \frac{4 π}{3} r^{3}$ Gravitational force, $F = G \frac{M_{1} M_{2}}{R^{2}}$
$∴$ Sphere are kept in contact each other so that the centre distance is $2 r$
$F = G \frac{ρ^{2} {(\frac{4}{3} π r^{3})}^{2}}{(2 r)^{2}}$
$F = \frac{1}{9} π^{2} ρ^{2} r^{4} G$
So, $F \propto ρ^{2} r^{4}$

MP PET -2013

Gravitation

138262 A point mass $m$ is placed inside a spherical shell of radius $R$ and mass $M$ at a distance $R / 2$ from the centre of the shell. The gravitational force exerted by the shell on the point mass is-

1

\frac{GMm}{R^{2}}

2

- \frac{GMm}{R^{2}}

3 Zero

4

4 \frac{GMm}{R^{2}}

Explanation:

C
If a point mass is placed inside a uniform spherical shell, the gravitational force on the point mass is zero. Hence, the gravitational force exerted by the shell on the point mass is zero.
$E_{Inside} = 0$
$So, F = {mE}_{Inside} = 0$

CG PET-22.05.2022

Gravitation

138267 The weight of a body is $9.8 N$ at the place where $g = 9.8 {ms}^{- 2}$ . Its mass is

1 Zero

2

9.8 kg

3

10 kg

4

1 kg

Explanation:

D $Given,$
$W = 9.8 N, and g = 9.8 m / s^{2}$
$Weight (W) = mg$
$Hence, (m) = \frac{W}{g} = \frac{9.8}{9.8} = 1 kg$

NDA (II) 2009

Gravitation

138257 Two spheres of mass $m$ and $M$ are situated in air and the gravitational force between them is 'f. The space around the masses is now filled with of specific gravity 4. The gravitational force will now be

1

4 f

2

f / 4

3

f / 16

4

f

Explanation:

D Let the distance between the two masses be R. Then, $f = \frac{GMm}{R^{2}}$
Since, gravitational force is independent of specific gravity of the surrounding medium.
$∴$ The gravitational force will be $f$ .

BCECE 2013

Gravitation

138258 Two identical solid spheres each of radius $r$ and made up of the material of density $ρ$ are kept in contact with each other. The gravitational force between the two spheres will be proportional to:

1

ρ^{2} r^{4}

2

ρ^{4} r^{2}

3

ρ^{2} r^{3}

4

ρ^{3} r^{2}

Explanation:

A Mass of each sphere $M_{1} = M_{2} = ρ \cdot V = ρ \frac{4 π}{3} r^{3}$ Gravitational force, $F = G \frac{M_{1} M_{2}}{R^{2}}$
$∴$ Sphere are kept in contact each other so that the centre distance is $2 r$
$F = G \frac{ρ^{2} {(\frac{4}{3} π r^{3})}^{2}}{(2 r)^{2}}$
$F = \frac{1}{9} π^{2} ρ^{2} r^{4} G$
So, $F \propto ρ^{2} r^{4}$

MP PET -2013

Gravitation

138262 A point mass $m$ is placed inside a spherical shell of radius $R$ and mass $M$ at a distance $R / 2$ from the centre of the shell. The gravitational force exerted by the shell on the point mass is-

1

\frac{GMm}{R^{2}}

2

- \frac{GMm}{R^{2}}

3 Zero

4

4 \frac{GMm}{R^{2}}

Explanation:

C
If a point mass is placed inside a uniform spherical shell, the gravitational force on the point mass is zero. Hence, the gravitational force exerted by the shell on the point mass is zero.
$E_{Inside} = 0$
$So, F = {mE}_{Inside} = 0$

CG PET-22.05.2022

Gravitation

138267 The weight of a body is $9.8 N$ at the place where $g = 9.8 {ms}^{- 2}$ . Its mass is

1 Zero

2

9.8 kg

3

10 kg

4

1 kg

Explanation:

D $Given,$
$W = 9.8 N, and g = 9.8 m / s^{2}$
$Weight (W) = mg$
$Hence, (m) = \frac{W}{g} = \frac{9.8}{9.8} = 1 kg$

NDA (II) 2009