Gravitational Field

Q. The value of acceleration due to gravity at certain height $h$ above the surface of the earth is $\frac{g}{4}$ , where $g$ is the value of acceleration due to gravity at the surface of the earth. The height $h$ is ($R$ is the radius of earth)

1. $R$
2. $2R$
3. $3R$
4. $4R$

Q.

What do you mean by geostationary satellite?

Q. If the radius of the earth decreases by 10%, the mass remaining unchanged, then acceleration due to gravity will

1. decreases by 19 %
2. decreases by more than 19 %
3. increases by 19 %
4. increases by more than 19 %

Q. The gravitational potential due to a mass distribution is $V=\frac{A}{\sqrt{x^2+a^2}}$. The gravitational field due to the mass distribution is

1. $\frac{Ax}{(x^2+a^2{)}^{\frac{3}{2}}}$
2. $\frac{2Ax}{(x^2+a^2{)}^{\frac{3}{2}}}$
3. $\frac{4Ax}{(x^2+a^2{)}^{\frac{3}{2}}}$
4. $\frac{8Ax}{(x^2+a^2{)}^{\frac{3}{2}}}$

Q. Four identical particles of mass $M$ are located at the corners of a square of side ${}^{\prime }{a}^{\prime }$. What should be their speed if each of them revolves under the influence of the others' gravitational field in a circular orbit circumscribing the square?

1. $1.21\sqrt{\frac{GM}{a}}$
2. $1.41\sqrt{\frac{GM}{a}}$
3. $1.16\sqrt{\frac{GM}{a}}$
4. $1.35\sqrt{\frac{GM}{a}}$

Q. Three identical particles each of mass m are placed at the three corners of an equilateral triangle of side "a". Find the gravitational force exerted on one body due to the other two

Q. Two bodies of masses $M_1$ and $M_2$ are placed at a distance $R$ apart. Then at the position where the gravitational field due to them is zero, the gravitational potential is

1. $-\frac{G\sqrt{M_1}}{R}$
2. $-\frac{G\sqrt{M_2}}{R}$
3. $-\frac{G(\sqrt{M_1}+\sqrt{M_2}{)}^2}{R}$
4. $-\frac{G(\sqrt{M_1}-\sqrt{M_2}{)}^2}{R}$

Q. Two bodies of masses $m$ and $4m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field is zero, is

1. $-\frac{4Gm}{r}$
2. $-\frac{6Gm}{r}$
3. $-\frac{9Gm}{r}$
4. Zero

Q.

Acceleration due to gravity is $g$ on the surface of the earth. Then, the value of the acceleration due to gravity at a height of $32km$ above earths surface is (assume radius of earth to be $6400km$)

1. $0.99gm{s}^{-2}$

2. $0.8gm{s}^{-2}$

3. $1.01gm{s}^{-2}$

4. $0.9gm{s}^{-2}$

Q. Four particles each of mass M, are located at the vertices of a square with side L. The gravitational potential due to this at the centre of the square is

1. 
2. 
3. 
4. 

Q.

The ratio of acceleration due to gravity at a depth h below the surface of earth and at a height h above the surface of earth for h << radius of earth

1. Decreases

2. Increases linearly with h

3. Is constant

4. Increases parabolically with h

Q. In a certain region of space, the gravitational field is given by $-\frac{k}{r}$, where $r$ is the distance and $k$ is a constant. If the gravitational potential at $r=r_0$ be $V_0$, then what is the expression for the gravitational potential $V$?

1. $k\text{ln}\frac{r}{r_0}$
2. $k\text{ln}\frac{r_0}{r}$
3. $V_0+k\text{ln}\frac{r}{r_0}$
4. $V_0+k\text{ln}\frac{r_0}{r}$

Q. The ratio of acceleration due to gravity at a height 3R above earth's surface to the acceleration due to the gravity on the surface of the earth is:

1. $\frac{1}{9}$
2. $\frac{1}{3}$
3. $\frac{1}{4}$
4. $\frac{1}{16}$

Q.

A long metal rod of length $l$ and relative density $\sigma$ is held vertically with its lower end just touching the surface of water. The speed of the rod when it just sinks in water is given by

1. $\sqrt{2gl}$

2. $\sqrt{2gl\sigma }$

3. $\sqrt{2gl(1-\frac{1}{2\sigma })}$

4. $\sqrt{2gl(2\sigma -1)}$

Q. Comparing the L-C oscillations with the oscillations of a spring- block system (force constant of spring = k and mass of block = m), the physical quantity mk is similar to :- (1) CL (2) 1/CL (3) C/L (4) L/C

Q.

The density inside a solid sphere of radius a is given by $\rho$ =${\rho }_0$a/r where ${\rho }_0$ is the density at the surface and r denotes the distance from the centre. The gravitational field due to this sphere at a distance 2a form its centre is..

1. 

2. 

3. 

4. 

Q.

If there were a smaller gravitational effect, which of the following forces do you think would alter in some respect

1. Archimedes uplift

2. Electrostatic force

3. None of the above

4. Viscous forces

Q.

At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the ay in this situation?

Q.

The acceleration due to gravity depends on

1. mass of the planet.

2. radius of the planet.

3. mass and radius of the planet.

4. none.

Q.

A geostationary satellite

1. Revolves about the polar axis

2. Is stationary in the space

3. Has a time period less than that of the near earth satellite

4. Moves faster than a near earth satellite

Q.

On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by $\frac{Ax}{{\left(x^2+a^2\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$ in the x-direction. The magnitude of gravitational potential on the x-axis at a distance x, taking its value to be zero at infinity, is:

1. $A{\left(x^2+a^2\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

2. $\frac{A}{{\left(x^2+a^2\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

3. $A{\left(x^2+a^2\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

4. $\frac{A}{{\left(x^2+a^2\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

Q. Gravitational field in $x-y$ plane is given as $\overrightarrow{g}=(2x\hat{i}+3y^2\hat{j})\text{N/kg}$. The difference in gravitational potential between $2$ points $\text{A}(2,4)$ & $\text{B}(6,0)$ is

1. $V_A-V_B=32\text{J/kg}$
2. $V_A-V_B=64\text{J/kg}$
3. $V_A-V_B=-64\text{J/kg}$
4. $V_A-V_B=-32\text{J/kg}$

Q. On the planet whose size is the same and mass four times, as that of earth, find the amount of work (in $J$) done to lift $3\text{kg}$ mass vertically upwards through $3\text{m}$ distance on the planet. (The value of $g$ on the surface of earth is $10{\text{ms}}^{-2}$)

Q. A spherical shell is cut into two pieces along a chord and separated by a large distance as shown in figure. For points $A$ and $B$, where $V$ and $\overrightarrow{E}$ are gravitational potential and field respectively, then

1. $V_A=V_B\text{and}|{\overrightarrow{E}}_A|>|{\overrightarrow{E}}_B|$
2. $V_A>V_B\text{and}|{\overrightarrow{E}}_A|<|{\overrightarrow{E}}_B|$
3. $V_A=V_B\text{and}|{\overrightarrow{E}}_A|=|{\overrightarrow{E}}_B|$
4. $V_A<V_B\text{and}|{\overrightarrow{E}}_A|=|{\overrightarrow{E}}_B|$

Q. Two particles each of mass M are connected at the two ends of a spring of force constant K . The whole system lie on a smooth horizontal plane . If the particles are pushed to compressed the spring and then released , then frequency of oscillation is?

Q.

There are two bodies of masses $100\text{kg}$ and $10000\text{kg}$ separated by a distance of $1\text{m}$. At what distance from the smaller body, the intensity of the gravitational field will be zero?

Q.

A: The satellites whose orbit is parallel to the equator are said to have an equatorial orbit.

R: The equatorial orbit of a satellite is useful for mineral prospecting.

1. Both ‘A’ and ‘R’ are correct and ‘R’ is the correct explanation of ‘A’.

2. Both ‘A’ and ‘R’ are correct and ‘R’ is not the correct explanation of ‘A’.

3. ‘A’ is correct, but ‘R’ is incorrect.

4. ‘A’ is incorrect, but ‘R’ is correct.

Q.

What are the three types of orbits of Earth?

Q.

Show that the value of $g$decreases as we go to higher altitudes above the surface of the earth. Mention one practical application of this property of $g$

Q.

The difference in the readings shown by a spring balance for a body of mass 40 kg on the surface of the Earth and a planet of mass half of that of the Earth and radius twice that of the Earth is __________ N (Take g = 10 m s^-2).

1. 320

2. 3200

3. 350

4. 500