138664
Two satellites of earth, $S_{1}$ and $S_{2}$, are moving in the same orbit. The mass of $S_{1}$ is four times the mass of $S_{2}$. Which one of the following statements is true?
1 The time period of $S_{1}$ is four times that of $S_{2}$
2 The potential energies of earth and satellite in the two cases are equal
3 $S_{1}$ and $S_{2}$ are moving with the same speed
4 The kinetic energies of the two satellites are equal
Explanation:
C In same orbit, orbital speed of satellites remains same. When two satellites of earth are moving in same orbit, then time period of both are equal. From Kepler's third law $\mathrm{T}^{2} \propto \mathrm{r}^{3}$ Time period is independent of mass, hence their time period will be equal. The potential energy and kinetic energy are mass dependent, hence the PE and KE of satellites are not equal. But, if they are orbiting in a same orbit, then they have equal orbital speed.
JIPMER 2009
Gravitation
138607
A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then
1 the acceleration of $\mathrm{S}$ is always directed towards the centre of the earth
2 the angular momentum of $\mathrm{S}$ about the centre of the earth changes in direction, but its magnitude remains constant
3 the total mechanical energy of $\mathrm{S}$ varies periodically with time
4 the linear momentum of S remains constant in magnitude
Explanation:
A The gravitational force on satellite due to earth acts always towards the centre of the earth, net torque of this gravitational force $\mathrm{F}$ about centre of earth is zero. Therefore, angular momentum of $\mathrm{S}$ about centre of earth is constant throughout. So, acceleration of satellite $\mathrm{S}$ is always directed towards centre of earth.
AIIMS-2010
Gravitation
138608
The difference in the length of a mean solar day and a sidereal day is about:
1 1 minute
2 4 minute
3 15 minute
4 56 minute
Explanation:
B Time taken by earth to complete one rotation about its axis $\rightarrow$ solar day. There is a difference of 4 minutes between solar day and sidereal day. 24 hours a day $\rightarrow 4$ min difference.
AIIMS-2003
Gravitation
138613
Consider the following statements: 1.During the motion around the sun in elliptical orbit, the total mechanical energy of the earth remains constant. 2.The gravitational field in which the earth moves is a conservative force field. Which of the above statements is/are correct?
1 1 only
2 2 only
3 Both 1 and 2
4 Neither 1 nor 2
Explanation:
C The total mechanical energy remains constant. Gravity field is conservative field. Hence both (1) \& (2) are correct.
SCRA-2012
Gravitation
138615
Two planets are at distances $R_{1}$ and $R_{2}$ from the sun, their periods are $T_{1}$ and $T_{2},\left(\frac{T_{1}}{T_{2}}\right)^{2}$ is equal to
C Two planets are at distances $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ from the sun, Their periods are $T_{1}$ and $T_{2},\left(\frac{T_{1}}{T_{2}}\right)^{2}$ is equal to $\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{3}$ From Kepler's third law, $\mathrm{T}^{2} \propto \mathrm{R}^{3}$ $\therefore\left(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right)^{2}=\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{3}$
138664
Two satellites of earth, $S_{1}$ and $S_{2}$, are moving in the same orbit. The mass of $S_{1}$ is four times the mass of $S_{2}$. Which one of the following statements is true?
1 The time period of $S_{1}$ is four times that of $S_{2}$
2 The potential energies of earth and satellite in the two cases are equal
3 $S_{1}$ and $S_{2}$ are moving with the same speed
4 The kinetic energies of the two satellites are equal
Explanation:
C In same orbit, orbital speed of satellites remains same. When two satellites of earth are moving in same orbit, then time period of both are equal. From Kepler's third law $\mathrm{T}^{2} \propto \mathrm{r}^{3}$ Time period is independent of mass, hence their time period will be equal. The potential energy and kinetic energy are mass dependent, hence the PE and KE of satellites are not equal. But, if they are orbiting in a same orbit, then they have equal orbital speed.
JIPMER 2009
Gravitation
138607
A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then
1 the acceleration of $\mathrm{S}$ is always directed towards the centre of the earth
2 the angular momentum of $\mathrm{S}$ about the centre of the earth changes in direction, but its magnitude remains constant
3 the total mechanical energy of $\mathrm{S}$ varies periodically with time
4 the linear momentum of S remains constant in magnitude
Explanation:
A The gravitational force on satellite due to earth acts always towards the centre of the earth, net torque of this gravitational force $\mathrm{F}$ about centre of earth is zero. Therefore, angular momentum of $\mathrm{S}$ about centre of earth is constant throughout. So, acceleration of satellite $\mathrm{S}$ is always directed towards centre of earth.
AIIMS-2010
Gravitation
138608
The difference in the length of a mean solar day and a sidereal day is about:
1 1 minute
2 4 minute
3 15 minute
4 56 minute
Explanation:
B Time taken by earth to complete one rotation about its axis $\rightarrow$ solar day. There is a difference of 4 minutes between solar day and sidereal day. 24 hours a day $\rightarrow 4$ min difference.
AIIMS-2003
Gravitation
138613
Consider the following statements: 1.During the motion around the sun in elliptical orbit, the total mechanical energy of the earth remains constant. 2.The gravitational field in which the earth moves is a conservative force field. Which of the above statements is/are correct?
1 1 only
2 2 only
3 Both 1 and 2
4 Neither 1 nor 2
Explanation:
C The total mechanical energy remains constant. Gravity field is conservative field. Hence both (1) \& (2) are correct.
SCRA-2012
Gravitation
138615
Two planets are at distances $R_{1}$ and $R_{2}$ from the sun, their periods are $T_{1}$ and $T_{2},\left(\frac{T_{1}}{T_{2}}\right)^{2}$ is equal to
C Two planets are at distances $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ from the sun, Their periods are $T_{1}$ and $T_{2},\left(\frac{T_{1}}{T_{2}}\right)^{2}$ is equal to $\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{3}$ From Kepler's third law, $\mathrm{T}^{2} \propto \mathrm{R}^{3}$ $\therefore\left(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right)^{2}=\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{3}$
138664
Two satellites of earth, $S_{1}$ and $S_{2}$, are moving in the same orbit. The mass of $S_{1}$ is four times the mass of $S_{2}$. Which one of the following statements is true?
1 The time period of $S_{1}$ is four times that of $S_{2}$
2 The potential energies of earth and satellite in the two cases are equal
3 $S_{1}$ and $S_{2}$ are moving with the same speed
4 The kinetic energies of the two satellites are equal
Explanation:
C In same orbit, orbital speed of satellites remains same. When two satellites of earth are moving in same orbit, then time period of both are equal. From Kepler's third law $\mathrm{T}^{2} \propto \mathrm{r}^{3}$ Time period is independent of mass, hence their time period will be equal. The potential energy and kinetic energy are mass dependent, hence the PE and KE of satellites are not equal. But, if they are orbiting in a same orbit, then they have equal orbital speed.
JIPMER 2009
Gravitation
138607
A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then
1 the acceleration of $\mathrm{S}$ is always directed towards the centre of the earth
2 the angular momentum of $\mathrm{S}$ about the centre of the earth changes in direction, but its magnitude remains constant
3 the total mechanical energy of $\mathrm{S}$ varies periodically with time
4 the linear momentum of S remains constant in magnitude
Explanation:
A The gravitational force on satellite due to earth acts always towards the centre of the earth, net torque of this gravitational force $\mathrm{F}$ about centre of earth is zero. Therefore, angular momentum of $\mathrm{S}$ about centre of earth is constant throughout. So, acceleration of satellite $\mathrm{S}$ is always directed towards centre of earth.
AIIMS-2010
Gravitation
138608
The difference in the length of a mean solar day and a sidereal day is about:
1 1 minute
2 4 minute
3 15 minute
4 56 minute
Explanation:
B Time taken by earth to complete one rotation about its axis $\rightarrow$ solar day. There is a difference of 4 minutes between solar day and sidereal day. 24 hours a day $\rightarrow 4$ min difference.
AIIMS-2003
Gravitation
138613
Consider the following statements: 1.During the motion around the sun in elliptical orbit, the total mechanical energy of the earth remains constant. 2.The gravitational field in which the earth moves is a conservative force field. Which of the above statements is/are correct?
1 1 only
2 2 only
3 Both 1 and 2
4 Neither 1 nor 2
Explanation:
C The total mechanical energy remains constant. Gravity field is conservative field. Hence both (1) \& (2) are correct.
SCRA-2012
Gravitation
138615
Two planets are at distances $R_{1}$ and $R_{2}$ from the sun, their periods are $T_{1}$ and $T_{2},\left(\frac{T_{1}}{T_{2}}\right)^{2}$ is equal to
C Two planets are at distances $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ from the sun, Their periods are $T_{1}$ and $T_{2},\left(\frac{T_{1}}{T_{2}}\right)^{2}$ is equal to $\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{3}$ From Kepler's third law, $\mathrm{T}^{2} \propto \mathrm{R}^{3}$ $\therefore\left(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right)^{2}=\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{3}$
138664
Two satellites of earth, $S_{1}$ and $S_{2}$, are moving in the same orbit. The mass of $S_{1}$ is four times the mass of $S_{2}$. Which one of the following statements is true?
1 The time period of $S_{1}$ is four times that of $S_{2}$
2 The potential energies of earth and satellite in the two cases are equal
3 $S_{1}$ and $S_{2}$ are moving with the same speed
4 The kinetic energies of the two satellites are equal
Explanation:
C In same orbit, orbital speed of satellites remains same. When two satellites of earth are moving in same orbit, then time period of both are equal. From Kepler's third law $\mathrm{T}^{2} \propto \mathrm{r}^{3}$ Time period is independent of mass, hence their time period will be equal. The potential energy and kinetic energy are mass dependent, hence the PE and KE of satellites are not equal. But, if they are orbiting in a same orbit, then they have equal orbital speed.
JIPMER 2009
Gravitation
138607
A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then
1 the acceleration of $\mathrm{S}$ is always directed towards the centre of the earth
2 the angular momentum of $\mathrm{S}$ about the centre of the earth changes in direction, but its magnitude remains constant
3 the total mechanical energy of $\mathrm{S}$ varies periodically with time
4 the linear momentum of S remains constant in magnitude
Explanation:
A The gravitational force on satellite due to earth acts always towards the centre of the earth, net torque of this gravitational force $\mathrm{F}$ about centre of earth is zero. Therefore, angular momentum of $\mathrm{S}$ about centre of earth is constant throughout. So, acceleration of satellite $\mathrm{S}$ is always directed towards centre of earth.
AIIMS-2010
Gravitation
138608
The difference in the length of a mean solar day and a sidereal day is about:
1 1 minute
2 4 minute
3 15 minute
4 56 minute
Explanation:
B Time taken by earth to complete one rotation about its axis $\rightarrow$ solar day. There is a difference of 4 minutes between solar day and sidereal day. 24 hours a day $\rightarrow 4$ min difference.
AIIMS-2003
Gravitation
138613
Consider the following statements: 1.During the motion around the sun in elliptical orbit, the total mechanical energy of the earth remains constant. 2.The gravitational field in which the earth moves is a conservative force field. Which of the above statements is/are correct?
1 1 only
2 2 only
3 Both 1 and 2
4 Neither 1 nor 2
Explanation:
C The total mechanical energy remains constant. Gravity field is conservative field. Hence both (1) \& (2) are correct.
SCRA-2012
Gravitation
138615
Two planets are at distances $R_{1}$ and $R_{2}$ from the sun, their periods are $T_{1}$ and $T_{2},\left(\frac{T_{1}}{T_{2}}\right)^{2}$ is equal to
C Two planets are at distances $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ from the sun, Their periods are $T_{1}$ and $T_{2},\left(\frac{T_{1}}{T_{2}}\right)^{2}$ is equal to $\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{3}$ From Kepler's third law, $\mathrm{T}^{2} \propto \mathrm{R}^{3}$ $\therefore\left(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right)^{2}=\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{3}$
138664
Two satellites of earth, $S_{1}$ and $S_{2}$, are moving in the same orbit. The mass of $S_{1}$ is four times the mass of $S_{2}$. Which one of the following statements is true?
1 The time period of $S_{1}$ is four times that of $S_{2}$
2 The potential energies of earth and satellite in the two cases are equal
3 $S_{1}$ and $S_{2}$ are moving with the same speed
4 The kinetic energies of the two satellites are equal
Explanation:
C In same orbit, orbital speed of satellites remains same. When two satellites of earth are moving in same orbit, then time period of both are equal. From Kepler's third law $\mathrm{T}^{2} \propto \mathrm{r}^{3}$ Time period is independent of mass, hence their time period will be equal. The potential energy and kinetic energy are mass dependent, hence the PE and KE of satellites are not equal. But, if they are orbiting in a same orbit, then they have equal orbital speed.
JIPMER 2009
Gravitation
138607
A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then
1 the acceleration of $\mathrm{S}$ is always directed towards the centre of the earth
2 the angular momentum of $\mathrm{S}$ about the centre of the earth changes in direction, but its magnitude remains constant
3 the total mechanical energy of $\mathrm{S}$ varies periodically with time
4 the linear momentum of S remains constant in magnitude
Explanation:
A The gravitational force on satellite due to earth acts always towards the centre of the earth, net torque of this gravitational force $\mathrm{F}$ about centre of earth is zero. Therefore, angular momentum of $\mathrm{S}$ about centre of earth is constant throughout. So, acceleration of satellite $\mathrm{S}$ is always directed towards centre of earth.
AIIMS-2010
Gravitation
138608
The difference in the length of a mean solar day and a sidereal day is about:
1 1 minute
2 4 minute
3 15 minute
4 56 minute
Explanation:
B Time taken by earth to complete one rotation about its axis $\rightarrow$ solar day. There is a difference of 4 minutes between solar day and sidereal day. 24 hours a day $\rightarrow 4$ min difference.
AIIMS-2003
Gravitation
138613
Consider the following statements: 1.During the motion around the sun in elliptical orbit, the total mechanical energy of the earth remains constant. 2.The gravitational field in which the earth moves is a conservative force field. Which of the above statements is/are correct?
1 1 only
2 2 only
3 Both 1 and 2
4 Neither 1 nor 2
Explanation:
C The total mechanical energy remains constant. Gravity field is conservative field. Hence both (1) \& (2) are correct.
SCRA-2012
Gravitation
138615
Two planets are at distances $R_{1}$ and $R_{2}$ from the sun, their periods are $T_{1}$ and $T_{2},\left(\frac{T_{1}}{T_{2}}\right)^{2}$ is equal to
C Two planets are at distances $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ from the sun, Their periods are $T_{1}$ and $T_{2},\left(\frac{T_{1}}{T_{2}}\right)^{2}$ is equal to $\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{3}$ From Kepler's third law, $\mathrm{T}^{2} \propto \mathrm{R}^{3}$ $\therefore\left(\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}\right)^{2}=\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{3}$
