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PHXI08:GRAVITATION

360018 $F_{g}, F_{e}$ and $F_{n}$ represent the gravitational, electromagnetic and nuclear forces respectively, then arrange the increasing order of their strengths

1

F_{n}, F_{e}, F_{g}

2

F_{g}, F_{e}, F_{n}

3

F_{e}, F_{g}, F_{n}

4

F_{g}, F_{n}, F_{e}

PHXI08:GRAVITATION

360019 Three masses, each equal to $M$ , are placed at the three corners of a square of side $a$ . The force of attraction on unit mass at the fourth corner will be

1

\frac{G M}{a^{2}} [\frac{1}{2} + \sqrt{2}]

2

\frac{3 G M}{a^{2}}

3

\frac{G M}{3 a^{2}}

4

\frac{G M}{a^{2}} \sqrt{3}

Explanation:

$F_{1} = F_{2} = \frac{G M}{a^{2}}$
Resultant of $F_{1}$ and $F_{2}$ is $\sqrt{2} \frac{G M}{a^{2}}$
supporting img
Now, $F_{3} = \frac{G M}{(\sqrt{2} a)^{2}} = \frac{G M}{2 a^{2}}$
Now, $\frac{\sqrt{2} G M}{a^{2}}$ and $\frac{G M}{2 a^{2}}$ act in the same direction. Their resultant is $\frac{G M}{a^{2}} [\sqrt{2} + \frac{1}{2}]$

PHXI08:GRAVITATION

360020 Particles of masses $2 M, m$ and $M$ are respectively at points $A$ , $B$ and $C$ with $A B = \frac{1}{2} (B C), m$ is much smaller than $M$ and at time $t = 0$ , they are all at rest as given in figure. At subsequent times before any collision takes place.
supporting img

1

m

will remain at rest

2

m

will move towards

M

3

m

will move towards 2

M

4

m

will have oscillatory motion

Explanation:

Resultant force on mass $m$ due to masses at $A$ and $C$ is $F = \frac{G 2 M \times m}{(A B^{2})} - \frac{G M m}{(B C^{2})}$ . Therfore, $m$ will move towards 2 $M$ .

NCERT Exemplar

PHXI08:GRAVITATION

360021 An astronaut of mass $m$ is working on a satellite orbiting the earth at a distance $h$ from the earth's surface. The radius of the earth is $R$ , while its mass is $M$ . The gravitational pull $F_{G}$ on the astronaut is

1 Zero since astronaut feels weightless

2

\frac{G M m}{(R + h)^{2}} < F_{G} < \frac{G M m}{R^{2}}

3

F_{G} = \frac{G M m}{(R + h)^{2}}

4

0 < F_{G} < \frac{G M m}{R^{2}}

Explanation:

Gravitational force $F = \frac{G M m}{(R + h)^{2}}$

JEE - 2016

PHXI08:GRAVITATION

360018 $F_{g}, F_{e}$ and $F_{n}$ represent the gravitational, electromagnetic and nuclear forces respectively, then arrange the increasing order of their strengths

1

F_{n}, F_{e}, F_{g}

2

F_{g}, F_{e}, F_{n}

3

F_{e}, F_{g}, F_{n}

4

F_{g}, F_{n}, F_{e}

PHXI08:GRAVITATION

360019 Three masses, each equal to $M$ , are placed at the three corners of a square of side $a$ . The force of attraction on unit mass at the fourth corner will be

1

\frac{G M}{a^{2}} [\frac{1}{2} + \sqrt{2}]

2

\frac{3 G M}{a^{2}}

3

\frac{G M}{3 a^{2}}

4

\frac{G M}{a^{2}} \sqrt{3}

Explanation:

$F_{1} = F_{2} = \frac{G M}{a^{2}}$
Resultant of $F_{1}$ and $F_{2}$ is $\sqrt{2} \frac{G M}{a^{2}}$
supporting img
Now, $F_{3} = \frac{G M}{(\sqrt{2} a)^{2}} = \frac{G M}{2 a^{2}}$
Now, $\frac{\sqrt{2} G M}{a^{2}}$ and $\frac{G M}{2 a^{2}}$ act in the same direction. Their resultant is $\frac{G M}{a^{2}} [\sqrt{2} + \frac{1}{2}]$

PHXI08:GRAVITATION

360020 Particles of masses $2 M, m$ and $M$ are respectively at points $A$ , $B$ and $C$ with $A B = \frac{1}{2} (B C), m$ is much smaller than $M$ and at time $t = 0$ , they are all at rest as given in figure. At subsequent times before any collision takes place.
supporting img

1

m

will remain at rest

2

m

will move towards

M

3

m

will move towards 2

M

4

m

will have oscillatory motion

Explanation:

Resultant force on mass $m$ due to masses at $A$ and $C$ is $F = \frac{G 2 M \times m}{(A B^{2})} - \frac{G M m}{(B C^{2})}$ . Therfore, $m$ will move towards 2 $M$ .

NCERT Exemplar

PHXI08:GRAVITATION

360021 An astronaut of mass $m$ is working on a satellite orbiting the earth at a distance $h$ from the earth's surface. The radius of the earth is $R$ , while its mass is $M$ . The gravitational pull $F_{G}$ on the astronaut is

1 Zero since astronaut feels weightless

2

\frac{G M m}{(R + h)^{2}} < F_{G} < \frac{G M m}{R^{2}}

3

F_{G} = \frac{G M m}{(R + h)^{2}}

4

0 < F_{G} < \frac{G M m}{R^{2}}

Explanation:

Gravitational force $F = \frac{G M m}{(R + h)^{2}}$

JEE - 2016

PHXI08:GRAVITATION

360018 $F_{g}, F_{e}$ and $F_{n}$ represent the gravitational, electromagnetic and nuclear forces respectively, then arrange the increasing order of their strengths

1

F_{n}, F_{e}, F_{g}

2

F_{g}, F_{e}, F_{n}

3

F_{e}, F_{g}, F_{n}

4

F_{g}, F_{n}, F_{e}

PHXI08:GRAVITATION

360019 Three masses, each equal to $M$ , are placed at the three corners of a square of side $a$ . The force of attraction on unit mass at the fourth corner will be

1

\frac{G M}{a^{2}} [\frac{1}{2} + \sqrt{2}]

2

\frac{3 G M}{a^{2}}

3

\frac{G M}{3 a^{2}}

4

\frac{G M}{a^{2}} \sqrt{3}

Explanation:

$F_{1} = F_{2} = \frac{G M}{a^{2}}$
Resultant of $F_{1}$ and $F_{2}$ is $\sqrt{2} \frac{G M}{a^{2}}$
supporting img
Now, $F_{3} = \frac{G M}{(\sqrt{2} a)^{2}} = \frac{G M}{2 a^{2}}$
Now, $\frac{\sqrt{2} G M}{a^{2}}$ and $\frac{G M}{2 a^{2}}$ act in the same direction. Their resultant is $\frac{G M}{a^{2}} [\sqrt{2} + \frac{1}{2}]$

PHXI08:GRAVITATION

360020 Particles of masses $2 M, m$ and $M$ are respectively at points $A$ , $B$ and $C$ with $A B = \frac{1}{2} (B C), m$ is much smaller than $M$ and at time $t = 0$ , they are all at rest as given in figure. At subsequent times before any collision takes place.
supporting img

1

m

will remain at rest

2

m

will move towards

M

3

m

will move towards 2

M

4

m

will have oscillatory motion

Explanation:

Resultant force on mass $m$ due to masses at $A$ and $C$ is $F = \frac{G 2 M \times m}{(A B^{2})} - \frac{G M m}{(B C^{2})}$ . Therfore, $m$ will move towards 2 $M$ .

NCERT Exemplar

PHXI08:GRAVITATION

360021 An astronaut of mass $m$ is working on a satellite orbiting the earth at a distance $h$ from the earth's surface. The radius of the earth is $R$ , while its mass is $M$ . The gravitational pull $F_{G}$ on the astronaut is

1 Zero since astronaut feels weightless

2

\frac{G M m}{(R + h)^{2}} < F_{G} < \frac{G M m}{R^{2}}

3

F_{G} = \frac{G M m}{(R + h)^{2}}

4

0 < F_{G} < \frac{G M m}{R^{2}}

Explanation:

Gravitational force $F = \frac{G M m}{(R + h)^{2}}$

JEE - 2016

PHXI08:GRAVITATION

360018 $F_{g}, F_{e}$ and $F_{n}$ represent the gravitational, electromagnetic and nuclear forces respectively, then arrange the increasing order of their strengths

1

F_{n}, F_{e}, F_{g}

2

F_{g}, F_{e}, F_{n}

3

F_{e}, F_{g}, F_{n}

4

F_{g}, F_{n}, F_{e}

PHXI08:GRAVITATION

360019 Three masses, each equal to $M$ , are placed at the three corners of a square of side $a$ . The force of attraction on unit mass at the fourth corner will be

1

\frac{G M}{a^{2}} [\frac{1}{2} + \sqrt{2}]

2

\frac{3 G M}{a^{2}}

3

\frac{G M}{3 a^{2}}

4

\frac{G M}{a^{2}} \sqrt{3}

Explanation:

$F_{1} = F_{2} = \frac{G M}{a^{2}}$
Resultant of $F_{1}$ and $F_{2}$ is $\sqrt{2} \frac{G M}{a^{2}}$
supporting img
Now, $F_{3} = \frac{G M}{(\sqrt{2} a)^{2}} = \frac{G M}{2 a^{2}}$
Now, $\frac{\sqrt{2} G M}{a^{2}}$ and $\frac{G M}{2 a^{2}}$ act in the same direction. Their resultant is $\frac{G M}{a^{2}} [\sqrt{2} + \frac{1}{2}]$

PHXI08:GRAVITATION

360020 Particles of masses $2 M, m$ and $M$ are respectively at points $A$ , $B$ and $C$ with $A B = \frac{1}{2} (B C), m$ is much smaller than $M$ and at time $t = 0$ , they are all at rest as given in figure. At subsequent times before any collision takes place.
supporting img

1

m

will remain at rest

2

m

will move towards

M

3

m

will move towards 2

M

4

m

will have oscillatory motion

Explanation:

Resultant force on mass $m$ due to masses at $A$ and $C$ is $F = \frac{G 2 M \times m}{(A B^{2})} - \frac{G M m}{(B C^{2})}$ . Therfore, $m$ will move towards 2 $M$ .

NCERT Exemplar

PHXI08:GRAVITATION

360021 An astronaut of mass $m$ is working on a satellite orbiting the earth at a distance $h$ from the earth's surface. The radius of the earth is $R$ , while its mass is $M$ . The gravitational pull $F_{G}$ on the astronaut is

1 Zero since astronaut feels weightless

2

\frac{G M m}{(R + h)^{2}} < F_{G} < \frac{G M m}{R^{2}}

3

F_{G} = \frac{G M m}{(R + h)^{2}}

4

0 < F_{G} < \frac{G M m}{R^{2}}

Explanation:

Gravitational force $F = \frac{G M m}{(R + h)^{2}}$

JEE - 2016

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