00. Newton's Law of Gravitation
Gravitation

138275 The magnitude of the gravitational force between a particle of mass $m_{1}$ and another particle of mass $m_{2}$ is $F(x)=\frac{G m_{1} m_{2}}{x^{2}}$
The work required to increase the separation of the particles from $x=x_{1}$ to $x_{1}+d$ is

1 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{x}_{1}}{\mathrm{~d}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
2 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{~d}}{\mathrm{x}_{1}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
3 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{x}_{1}^{2}}{\mathrm{~d}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
4 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{~d}^{2}}{\mathrm{x}_{1}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
Gravitation

138276 Let $F$ be the force of attraction between the earth and the sun. When the distance between them is increased to 3 times, then the force of attraction between them will be

1 $\frac{F}{9}$
2 $\mathrm{F}$
3 $\frac{\mathrm{F}}{4}$
4 $3 \mathrm{~F}$
Gravitation

138277 At what distance (in metre) from the centre of the Moon, the intensity of gravitational field will be zero? (Take, mass of Earth and Moon as $5.98 \times 10^{24} \mathrm{~kg}$ and $7.35 \times 10^{22} \mathrm{~kg}$ respectively and the distance between Moon and Earth is $\left.3.85 \times 10^{8} \mathrm{~m}\right)$

1 zero
2 $3.85 \times 10^{7}$
3 $8 \times 10^{8}$
4 $3.46 \times 10^{8}$
Gravitation

138279 Three identical particle $A, B$ and $C$ of mass 100 $\mathrm{kg}$ each are placed in a straight line with $A B=$ $B C=13 \mathrm{~m}$. The gravitational force on a fourth particle $P$ of the same mass is $F$, when placed at a distance $13 \mathrm{~m}$ from the particle $B$ on the perpendicular bisector of the line AC. The value of $F$ will be approximately:

1 $21 \mathrm{G}$
2 $100 \mathrm{G}$
3 $59 \mathrm{G}$
4 $42 \mathrm{G}$
Gravitation

138280 Infinite number of spheres, each of mass $m$ are placed on the $\mathrm{X}$-axis at distances $1,2,4,8,16 \ldots$. meters from origin. The Magnitude of the gravitational field at the origin is

1 $\frac{2}{3} \mathrm{Gm}$
2 $\frac{4}{3} \mathrm{Gm}$
3 $\mathrm{Gm}$
4 $6 \mathrm{Gm}$
Gravitation

138275 The magnitude of the gravitational force between a particle of mass $m_{1}$ and another particle of mass $m_{2}$ is $F(x)=\frac{G m_{1} m_{2}}{x^{2}}$
The work required to increase the separation of the particles from $x=x_{1}$ to $x_{1}+d$ is

1 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{x}_{1}}{\mathrm{~d}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
2 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{~d}}{\mathrm{x}_{1}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
3 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{x}_{1}^{2}}{\mathrm{~d}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
4 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{~d}^{2}}{\mathrm{x}_{1}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
Gravitation

138276 Let $F$ be the force of attraction between the earth and the sun. When the distance between them is increased to 3 times, then the force of attraction between them will be

1 $\frac{F}{9}$
2 $\mathrm{F}$
3 $\frac{\mathrm{F}}{4}$
4 $3 \mathrm{~F}$
Gravitation

138277 At what distance (in metre) from the centre of the Moon, the intensity of gravitational field will be zero? (Take, mass of Earth and Moon as $5.98 \times 10^{24} \mathrm{~kg}$ and $7.35 \times 10^{22} \mathrm{~kg}$ respectively and the distance between Moon and Earth is $\left.3.85 \times 10^{8} \mathrm{~m}\right)$

1 zero
2 $3.85 \times 10^{7}$
3 $8 \times 10^{8}$
4 $3.46 \times 10^{8}$
Gravitation

138279 Three identical particle $A, B$ and $C$ of mass 100 $\mathrm{kg}$ each are placed in a straight line with $A B=$ $B C=13 \mathrm{~m}$. The gravitational force on a fourth particle $P$ of the same mass is $F$, when placed at a distance $13 \mathrm{~m}$ from the particle $B$ on the perpendicular bisector of the line AC. The value of $F$ will be approximately:

1 $21 \mathrm{G}$
2 $100 \mathrm{G}$
3 $59 \mathrm{G}$
4 $42 \mathrm{G}$
Gravitation

138280 Infinite number of spheres, each of mass $m$ are placed on the $\mathrm{X}$-axis at distances $1,2,4,8,16 \ldots$. meters from origin. The Magnitude of the gravitational field at the origin is

1 $\frac{2}{3} \mathrm{Gm}$
2 $\frac{4}{3} \mathrm{Gm}$
3 $\mathrm{Gm}$
4 $6 \mathrm{Gm}$
Gravitation

138275 The magnitude of the gravitational force between a particle of mass $m_{1}$ and another particle of mass $m_{2}$ is $F(x)=\frac{G m_{1} m_{2}}{x^{2}}$
The work required to increase the separation of the particles from $x=x_{1}$ to $x_{1}+d$ is

1 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{x}_{1}}{\mathrm{~d}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
2 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{~d}}{\mathrm{x}_{1}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
3 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{x}_{1}^{2}}{\mathrm{~d}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
4 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{~d}^{2}}{\mathrm{x}_{1}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
Gravitation

138276 Let $F$ be the force of attraction between the earth and the sun. When the distance between them is increased to 3 times, then the force of attraction between them will be

1 $\frac{F}{9}$
2 $\mathrm{F}$
3 $\frac{\mathrm{F}}{4}$
4 $3 \mathrm{~F}$
Gravitation

138277 At what distance (in metre) from the centre of the Moon, the intensity of gravitational field will be zero? (Take, mass of Earth and Moon as $5.98 \times 10^{24} \mathrm{~kg}$ and $7.35 \times 10^{22} \mathrm{~kg}$ respectively and the distance between Moon and Earth is $\left.3.85 \times 10^{8} \mathrm{~m}\right)$

1 zero
2 $3.85 \times 10^{7}$
3 $8 \times 10^{8}$
4 $3.46 \times 10^{8}$
Gravitation

138279 Three identical particle $A, B$ and $C$ of mass 100 $\mathrm{kg}$ each are placed in a straight line with $A B=$ $B C=13 \mathrm{~m}$. The gravitational force on a fourth particle $P$ of the same mass is $F$, when placed at a distance $13 \mathrm{~m}$ from the particle $B$ on the perpendicular bisector of the line AC. The value of $F$ will be approximately:

1 $21 \mathrm{G}$
2 $100 \mathrm{G}$
3 $59 \mathrm{G}$
4 $42 \mathrm{G}$
Gravitation

138280 Infinite number of spheres, each of mass $m$ are placed on the $\mathrm{X}$-axis at distances $1,2,4,8,16 \ldots$. meters from origin. The Magnitude of the gravitational field at the origin is

1 $\frac{2}{3} \mathrm{Gm}$
2 $\frac{4}{3} \mathrm{Gm}$
3 $\mathrm{Gm}$
4 $6 \mathrm{Gm}$
Gravitation

138275 The magnitude of the gravitational force between a particle of mass $m_{1}$ and another particle of mass $m_{2}$ is $F(x)=\frac{G m_{1} m_{2}}{x^{2}}$
The work required to increase the separation of the particles from $x=x_{1}$ to $x_{1}+d$ is

1 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{x}_{1}}{\mathrm{~d}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
2 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{~d}}{\mathrm{x}_{1}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
3 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{x}_{1}^{2}}{\mathrm{~d}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
4 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{~d}^{2}}{\mathrm{x}_{1}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
Gravitation

138276 Let $F$ be the force of attraction between the earth and the sun. When the distance between them is increased to 3 times, then the force of attraction between them will be

1 $\frac{F}{9}$
2 $\mathrm{F}$
3 $\frac{\mathrm{F}}{4}$
4 $3 \mathrm{~F}$
Gravitation

138277 At what distance (in metre) from the centre of the Moon, the intensity of gravitational field will be zero? (Take, mass of Earth and Moon as $5.98 \times 10^{24} \mathrm{~kg}$ and $7.35 \times 10^{22} \mathrm{~kg}$ respectively and the distance between Moon and Earth is $\left.3.85 \times 10^{8} \mathrm{~m}\right)$

1 zero
2 $3.85 \times 10^{7}$
3 $8 \times 10^{8}$
4 $3.46 \times 10^{8}$
Gravitation

138279 Three identical particle $A, B$ and $C$ of mass 100 $\mathrm{kg}$ each are placed in a straight line with $A B=$ $B C=13 \mathrm{~m}$. The gravitational force on a fourth particle $P$ of the same mass is $F$, when placed at a distance $13 \mathrm{~m}$ from the particle $B$ on the perpendicular bisector of the line AC. The value of $F$ will be approximately:

1 $21 \mathrm{G}$
2 $100 \mathrm{G}$
3 $59 \mathrm{G}$
4 $42 \mathrm{G}$
Gravitation

138280 Infinite number of spheres, each of mass $m$ are placed on the $\mathrm{X}$-axis at distances $1,2,4,8,16 \ldots$. meters from origin. The Magnitude of the gravitational field at the origin is

1 $\frac{2}{3} \mathrm{Gm}$
2 $\frac{4}{3} \mathrm{Gm}$
3 $\mathrm{Gm}$
4 $6 \mathrm{Gm}$
Gravitation

138275 The magnitude of the gravitational force between a particle of mass $m_{1}$ and another particle of mass $m_{2}$ is $F(x)=\frac{G m_{1} m_{2}}{x^{2}}$
The work required to increase the separation of the particles from $x=x_{1}$ to $x_{1}+d$ is

1 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{x}_{1}}{\mathrm{~d}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
2 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{~d}}{\mathrm{x}_{1}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
3 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{x}_{1}^{2}}{\mathrm{~d}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
4 $\frac{\mathrm{Gm}_{1} \mathrm{~m}_{2} \mathrm{~d}^{2}}{\mathrm{x}_{1}\left(\mathrm{x}_{1}+\mathrm{d}\right)}$
Gravitation

138276 Let $F$ be the force of attraction between the earth and the sun. When the distance between them is increased to 3 times, then the force of attraction between them will be

1 $\frac{F}{9}$
2 $\mathrm{F}$
3 $\frac{\mathrm{F}}{4}$
4 $3 \mathrm{~F}$
Gravitation

138277 At what distance (in metre) from the centre of the Moon, the intensity of gravitational field will be zero? (Take, mass of Earth and Moon as $5.98 \times 10^{24} \mathrm{~kg}$ and $7.35 \times 10^{22} \mathrm{~kg}$ respectively and the distance between Moon and Earth is $\left.3.85 \times 10^{8} \mathrm{~m}\right)$

1 zero
2 $3.85 \times 10^{7}$
3 $8 \times 10^{8}$
4 $3.46 \times 10^{8}$
Gravitation

138279 Three identical particle $A, B$ and $C$ of mass 100 $\mathrm{kg}$ each are placed in a straight line with $A B=$ $B C=13 \mathrm{~m}$. The gravitational force on a fourth particle $P$ of the same mass is $F$, when placed at a distance $13 \mathrm{~m}$ from the particle $B$ on the perpendicular bisector of the line AC. The value of $F$ will be approximately:

1 $21 \mathrm{G}$
2 $100 \mathrm{G}$
3 $59 \mathrm{G}$
4 $42 \mathrm{G}$
Gravitation

138280 Infinite number of spheres, each of mass $m$ are placed on the $\mathrm{X}$-axis at distances $1,2,4,8,16 \ldots$. meters from origin. The Magnitude of the gravitational field at the origin is

1 $\frac{2}{3} \mathrm{Gm}$
2 $\frac{4}{3} \mathrm{Gm}$
3 $\mathrm{Gm}$
4 $6 \mathrm{Gm}$