00. Newton's Law of Gravitation
Gravitation

138255 A point mass ' $m$ ' is located at a distance $r$ from a uniform thin rod of mass $M$ and length $L$ as shown in the figure. The magnitude of gravitational force of attraction is

1 $\frac{\mathrm{GMm}}{\mathrm{r}^{2}}$
2 $\frac{\mathrm{GMm}}{(\mathrm{r}+\mathrm{L})^{2}}$
3 $\frac{\mathrm{GMm}}{\mathrm{r}(\mathrm{r}+\mathrm{L})}$
4 $\frac{\mathrm{GMm}}{\left(\mathrm{r}+\frac{\mathrm{L}}{2}\right)^{2}}$
Gravitation

138256 For identical masses of $m$ are kept at corners of a square. If the gravitational force exerted on one of masses by the other masses is $\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{G^{2}}{L^{2}}$, then the length of the side of the square is

1 $\mathrm{L}$
2 $2 \mathrm{~L}$
3 $4 \mathrm{~L}$
4 $\mathrm{L} / 2$
Gravitation

138259 In a gravitational force field a particle is taken from $A$ to $B$ along different paths as shown in figure. Then

1 Work done along path I will be maximum
2 Work done along path III with be minimum
3 Work done along path IV will be minimum
4 Work done along all the paths will be the same
Gravitation

138260 A solid sphere of radius $R$ gravitationally attracts a particle of mass $m$ at a distance $3 R$ from its centre such that the force is $F_{1}$. Now a spherical cavity of radius $\frac{R}{2}$ is extracted (as shown in the figure below) from the sphere and the force becomes $F_{2}$. The value of $\frac{F_{1}}{F_{2}}$ is

1 $41 / 50$
2 $50 / 41$
3 $25 / 36$
4 $36 / 25$
Gravitation

138255 A point mass ' $m$ ' is located at a distance $r$ from a uniform thin rod of mass $M$ and length $L$ as shown in the figure. The magnitude of gravitational force of attraction is

1 $\frac{\mathrm{GMm}}{\mathrm{r}^{2}}$
2 $\frac{\mathrm{GMm}}{(\mathrm{r}+\mathrm{L})^{2}}$
3 $\frac{\mathrm{GMm}}{\mathrm{r}(\mathrm{r}+\mathrm{L})}$
4 $\frac{\mathrm{GMm}}{\left(\mathrm{r}+\frac{\mathrm{L}}{2}\right)^{2}}$
Gravitation

138256 For identical masses of $m$ are kept at corners of a square. If the gravitational force exerted on one of masses by the other masses is $\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{G^{2}}{L^{2}}$, then the length of the side of the square is

1 $\mathrm{L}$
2 $2 \mathrm{~L}$
3 $4 \mathrm{~L}$
4 $\mathrm{L} / 2$
Gravitation

138259 In a gravitational force field a particle is taken from $A$ to $B$ along different paths as shown in figure. Then

1 Work done along path I will be maximum
2 Work done along path III with be minimum
3 Work done along path IV will be minimum
4 Work done along all the paths will be the same
Gravitation

138260 A solid sphere of radius $R$ gravitationally attracts a particle of mass $m$ at a distance $3 R$ from its centre such that the force is $F_{1}$. Now a spherical cavity of radius $\frac{R}{2}$ is extracted (as shown in the figure below) from the sphere and the force becomes $F_{2}$. The value of $\frac{F_{1}}{F_{2}}$ is

1 $41 / 50$
2 $50 / 41$
3 $25 / 36$
4 $36 / 25$
Gravitation

138255 A point mass ' $m$ ' is located at a distance $r$ from a uniform thin rod of mass $M$ and length $L$ as shown in the figure. The magnitude of gravitational force of attraction is

1 $\frac{\mathrm{GMm}}{\mathrm{r}^{2}}$
2 $\frac{\mathrm{GMm}}{(\mathrm{r}+\mathrm{L})^{2}}$
3 $\frac{\mathrm{GMm}}{\mathrm{r}(\mathrm{r}+\mathrm{L})}$
4 $\frac{\mathrm{GMm}}{\left(\mathrm{r}+\frac{\mathrm{L}}{2}\right)^{2}}$
Gravitation

138256 For identical masses of $m$ are kept at corners of a square. If the gravitational force exerted on one of masses by the other masses is $\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{G^{2}}{L^{2}}$, then the length of the side of the square is

1 $\mathrm{L}$
2 $2 \mathrm{~L}$
3 $4 \mathrm{~L}$
4 $\mathrm{L} / 2$
Gravitation

138259 In a gravitational force field a particle is taken from $A$ to $B$ along different paths as shown in figure. Then

1 Work done along path I will be maximum
2 Work done along path III with be minimum
3 Work done along path IV will be minimum
4 Work done along all the paths will be the same
Gravitation

138260 A solid sphere of radius $R$ gravitationally attracts a particle of mass $m$ at a distance $3 R$ from its centre such that the force is $F_{1}$. Now a spherical cavity of radius $\frac{R}{2}$ is extracted (as shown in the figure below) from the sphere and the force becomes $F_{2}$. The value of $\frac{F_{1}}{F_{2}}$ is

1 $41 / 50$
2 $50 / 41$
3 $25 / 36$
4 $36 / 25$
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Gravitation

138255 A point mass ' $m$ ' is located at a distance $r$ from a uniform thin rod of mass $M$ and length $L$ as shown in the figure. The magnitude of gravitational force of attraction is

1 $\frac{\mathrm{GMm}}{\mathrm{r}^{2}}$
2 $\frac{\mathrm{GMm}}{(\mathrm{r}+\mathrm{L})^{2}}$
3 $\frac{\mathrm{GMm}}{\mathrm{r}(\mathrm{r}+\mathrm{L})}$
4 $\frac{\mathrm{GMm}}{\left(\mathrm{r}+\frac{\mathrm{L}}{2}\right)^{2}}$
Gravitation

138256 For identical masses of $m$ are kept at corners of a square. If the gravitational force exerted on one of masses by the other masses is $\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{G^{2}}{L^{2}}$, then the length of the side of the square is

1 $\mathrm{L}$
2 $2 \mathrm{~L}$
3 $4 \mathrm{~L}$
4 $\mathrm{L} / 2$
Gravitation

138259 In a gravitational force field a particle is taken from $A$ to $B$ along different paths as shown in figure. Then

1 Work done along path I will be maximum
2 Work done along path III with be minimum
3 Work done along path IV will be minimum
4 Work done along all the paths will be the same
Gravitation

138260 A solid sphere of radius $R$ gravitationally attracts a particle of mass $m$ at a distance $3 R$ from its centre such that the force is $F_{1}$. Now a spherical cavity of radius $\frac{R}{2}$ is extracted (as shown in the figure below) from the sphere and the force becomes $F_{2}$. The value of $\frac{F_{1}}{F_{2}}$ is

1 $41 / 50$
2 $50 / 41$
3 $25 / 36$
4 $36 / 25$