359740
Assertion : The time period of geostationary satellite is 24 hours. Reason : Geostationary satellite must have the same time period as the time taken by the earth to complete one revolution about its axis.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
A geostationary satellite orbits at the same rotational speed as the Earth, which takes approximately 24 hours. Hence, appears to be stationary with respect to earth. So correct option is (1).
PHXI08:GRAVITATION
359741
The time period of a stationary satellite depends on I. Mass of the satellite II. Mass of the earth III. Radius of the orbit IV. Height of the satellite from the surface of the earth. Which of the following statement(s) is/are correct?
1 Only I
2 Both I and II
3 I, II and III
4 II, III and IV
Explanation:
Time period of satellite \(=\dfrac{2 \pi\left(R_{E}+h\right)^{3 / 2}}{\sqrt{G M_{E}}}\) From the above equation, it is evident that the time period of a satellite depends on mass of the earth \(\left(M_{E}\right)\), radius of the orbit \(\left(r=R_{E}+h\right)\) and height of the satellite from the surface of the earth \((h)\).
PHXI08:GRAVITATION
359742
Which of the following statement is correct regarding a geostationary satellite?
1 A geostationary satellite goes around the earth in east-west direction.
2 A geostationary satellite goes around the earth in west-east direction.
3 The time period of a geostationary satellite is 48 hours.
4 The angle between the equatorial plane and the orbital plane of geostationary satellite is \(90^{\circ}\).
Explanation:
A geostationary satellite goes around the earth in west-east direction. The time period a geostationary satellite is 24 hours. The angle between the equatorial plane and the orbital plane of geostationary satellite is \(0^{\circ}\).
PHXI08:GRAVITATION
359743
Assertion : Even when orbit of a satellite is elliptical. its plane of rotation passes through the centre of earth. Reason : According to law of conservation of angular momentum plane of rotation of satellite always remain same.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Gravitational force \(F\) is a central force, meaning that \(F\) is function of \(r\) only (whether orbit is circular or elliptical). If ellipse, earth must lie at one of its foci. Gravitational force is attractive, internal and conservative. As there is no torque acting on the planet, its angular momentum must remain constant both in magnitude and direction. The plane of rotation shall have the center of the Earth. So correct option is (1).
PHXI08:GRAVITATION
359744
The orbital angular momentum of a satellite is \(L\), when it is revolving in a circular orbit at height \(h\) from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be
1 \(8\,L\)
2 \(4\,L\)
3 \(3\,L\)
4 \(9\,L\)
Explanation:
\(L=m v r\) \(v=\) Orbital velocity where, \(v=\sqrt{\dfrac{G m}{r}}\) \(\Rightarrow L \propto \sqrt{r} \because L \propto v r\) \(L^{\prime}=8 r+r=9 r\) or \(L^{\prime} \propto 3 \sqrt{r}\). All other parameters are constant then, \(L^{\prime}=3 L\)
359740
Assertion : The time period of geostationary satellite is 24 hours. Reason : Geostationary satellite must have the same time period as the time taken by the earth to complete one revolution about its axis.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
A geostationary satellite orbits at the same rotational speed as the Earth, which takes approximately 24 hours. Hence, appears to be stationary with respect to earth. So correct option is (1).
PHXI08:GRAVITATION
359741
The time period of a stationary satellite depends on I. Mass of the satellite II. Mass of the earth III. Radius of the orbit IV. Height of the satellite from the surface of the earth. Which of the following statement(s) is/are correct?
1 Only I
2 Both I and II
3 I, II and III
4 II, III and IV
Explanation:
Time period of satellite \(=\dfrac{2 \pi\left(R_{E}+h\right)^{3 / 2}}{\sqrt{G M_{E}}}\) From the above equation, it is evident that the time period of a satellite depends on mass of the earth \(\left(M_{E}\right)\), radius of the orbit \(\left(r=R_{E}+h\right)\) and height of the satellite from the surface of the earth \((h)\).
PHXI08:GRAVITATION
359742
Which of the following statement is correct regarding a geostationary satellite?
1 A geostationary satellite goes around the earth in east-west direction.
2 A geostationary satellite goes around the earth in west-east direction.
3 The time period of a geostationary satellite is 48 hours.
4 The angle between the equatorial plane and the orbital plane of geostationary satellite is \(90^{\circ}\).
Explanation:
A geostationary satellite goes around the earth in west-east direction. The time period a geostationary satellite is 24 hours. The angle between the equatorial plane and the orbital plane of geostationary satellite is \(0^{\circ}\).
PHXI08:GRAVITATION
359743
Assertion : Even when orbit of a satellite is elliptical. its plane of rotation passes through the centre of earth. Reason : According to law of conservation of angular momentum plane of rotation of satellite always remain same.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Gravitational force \(F\) is a central force, meaning that \(F\) is function of \(r\) only (whether orbit is circular or elliptical). If ellipse, earth must lie at one of its foci. Gravitational force is attractive, internal and conservative. As there is no torque acting on the planet, its angular momentum must remain constant both in magnitude and direction. The plane of rotation shall have the center of the Earth. So correct option is (1).
PHXI08:GRAVITATION
359744
The orbital angular momentum of a satellite is \(L\), when it is revolving in a circular orbit at height \(h\) from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be
1 \(8\,L\)
2 \(4\,L\)
3 \(3\,L\)
4 \(9\,L\)
Explanation:
\(L=m v r\) \(v=\) Orbital velocity where, \(v=\sqrt{\dfrac{G m}{r}}\) \(\Rightarrow L \propto \sqrt{r} \because L \propto v r\) \(L^{\prime}=8 r+r=9 r\) or \(L^{\prime} \propto 3 \sqrt{r}\). All other parameters are constant then, \(L^{\prime}=3 L\)
359740
Assertion : The time period of geostationary satellite is 24 hours. Reason : Geostationary satellite must have the same time period as the time taken by the earth to complete one revolution about its axis.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
A geostationary satellite orbits at the same rotational speed as the Earth, which takes approximately 24 hours. Hence, appears to be stationary with respect to earth. So correct option is (1).
PHXI08:GRAVITATION
359741
The time period of a stationary satellite depends on I. Mass of the satellite II. Mass of the earth III. Radius of the orbit IV. Height of the satellite from the surface of the earth. Which of the following statement(s) is/are correct?
1 Only I
2 Both I and II
3 I, II and III
4 II, III and IV
Explanation:
Time period of satellite \(=\dfrac{2 \pi\left(R_{E}+h\right)^{3 / 2}}{\sqrt{G M_{E}}}\) From the above equation, it is evident that the time period of a satellite depends on mass of the earth \(\left(M_{E}\right)\), radius of the orbit \(\left(r=R_{E}+h\right)\) and height of the satellite from the surface of the earth \((h)\).
PHXI08:GRAVITATION
359742
Which of the following statement is correct regarding a geostationary satellite?
1 A geostationary satellite goes around the earth in east-west direction.
2 A geostationary satellite goes around the earth in west-east direction.
3 The time period of a geostationary satellite is 48 hours.
4 The angle between the equatorial plane and the orbital plane of geostationary satellite is \(90^{\circ}\).
Explanation:
A geostationary satellite goes around the earth in west-east direction. The time period a geostationary satellite is 24 hours. The angle between the equatorial plane and the orbital plane of geostationary satellite is \(0^{\circ}\).
PHXI08:GRAVITATION
359743
Assertion : Even when orbit of a satellite is elliptical. its plane of rotation passes through the centre of earth. Reason : According to law of conservation of angular momentum plane of rotation of satellite always remain same.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Gravitational force \(F\) is a central force, meaning that \(F\) is function of \(r\) only (whether orbit is circular or elliptical). If ellipse, earth must lie at one of its foci. Gravitational force is attractive, internal and conservative. As there is no torque acting on the planet, its angular momentum must remain constant both in magnitude and direction. The plane of rotation shall have the center of the Earth. So correct option is (1).
PHXI08:GRAVITATION
359744
The orbital angular momentum of a satellite is \(L\), when it is revolving in a circular orbit at height \(h\) from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be
1 \(8\,L\)
2 \(4\,L\)
3 \(3\,L\)
4 \(9\,L\)
Explanation:
\(L=m v r\) \(v=\) Orbital velocity where, \(v=\sqrt{\dfrac{G m}{r}}\) \(\Rightarrow L \propto \sqrt{r} \because L \propto v r\) \(L^{\prime}=8 r+r=9 r\) or \(L^{\prime} \propto 3 \sqrt{r}\). All other parameters are constant then, \(L^{\prime}=3 L\)
359740
Assertion : The time period of geostationary satellite is 24 hours. Reason : Geostationary satellite must have the same time period as the time taken by the earth to complete one revolution about its axis.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
A geostationary satellite orbits at the same rotational speed as the Earth, which takes approximately 24 hours. Hence, appears to be stationary with respect to earth. So correct option is (1).
PHXI08:GRAVITATION
359741
The time period of a stationary satellite depends on I. Mass of the satellite II. Mass of the earth III. Radius of the orbit IV. Height of the satellite from the surface of the earth. Which of the following statement(s) is/are correct?
1 Only I
2 Both I and II
3 I, II and III
4 II, III and IV
Explanation:
Time period of satellite \(=\dfrac{2 \pi\left(R_{E}+h\right)^{3 / 2}}{\sqrt{G M_{E}}}\) From the above equation, it is evident that the time period of a satellite depends on mass of the earth \(\left(M_{E}\right)\), radius of the orbit \(\left(r=R_{E}+h\right)\) and height of the satellite from the surface of the earth \((h)\).
PHXI08:GRAVITATION
359742
Which of the following statement is correct regarding a geostationary satellite?
1 A geostationary satellite goes around the earth in east-west direction.
2 A geostationary satellite goes around the earth in west-east direction.
3 The time period of a geostationary satellite is 48 hours.
4 The angle between the equatorial plane and the orbital plane of geostationary satellite is \(90^{\circ}\).
Explanation:
A geostationary satellite goes around the earth in west-east direction. The time period a geostationary satellite is 24 hours. The angle between the equatorial plane and the orbital plane of geostationary satellite is \(0^{\circ}\).
PHXI08:GRAVITATION
359743
Assertion : Even when orbit of a satellite is elliptical. its plane of rotation passes through the centre of earth. Reason : According to law of conservation of angular momentum plane of rotation of satellite always remain same.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Gravitational force \(F\) is a central force, meaning that \(F\) is function of \(r\) only (whether orbit is circular or elliptical). If ellipse, earth must lie at one of its foci. Gravitational force is attractive, internal and conservative. As there is no torque acting on the planet, its angular momentum must remain constant both in magnitude and direction. The plane of rotation shall have the center of the Earth. So correct option is (1).
PHXI08:GRAVITATION
359744
The orbital angular momentum of a satellite is \(L\), when it is revolving in a circular orbit at height \(h\) from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be
1 \(8\,L\)
2 \(4\,L\)
3 \(3\,L\)
4 \(9\,L\)
Explanation:
\(L=m v r\) \(v=\) Orbital velocity where, \(v=\sqrt{\dfrac{G m}{r}}\) \(\Rightarrow L \propto \sqrt{r} \because L \propto v r\) \(L^{\prime}=8 r+r=9 r\) or \(L^{\prime} \propto 3 \sqrt{r}\). All other parameters are constant then, \(L^{\prime}=3 L\)
359740
Assertion : The time period of geostationary satellite is 24 hours. Reason : Geostationary satellite must have the same time period as the time taken by the earth to complete one revolution about its axis.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
A geostationary satellite orbits at the same rotational speed as the Earth, which takes approximately 24 hours. Hence, appears to be stationary with respect to earth. So correct option is (1).
PHXI08:GRAVITATION
359741
The time period of a stationary satellite depends on I. Mass of the satellite II. Mass of the earth III. Radius of the orbit IV. Height of the satellite from the surface of the earth. Which of the following statement(s) is/are correct?
1 Only I
2 Both I and II
3 I, II and III
4 II, III and IV
Explanation:
Time period of satellite \(=\dfrac{2 \pi\left(R_{E}+h\right)^{3 / 2}}{\sqrt{G M_{E}}}\) From the above equation, it is evident that the time period of a satellite depends on mass of the earth \(\left(M_{E}\right)\), radius of the orbit \(\left(r=R_{E}+h\right)\) and height of the satellite from the surface of the earth \((h)\).
PHXI08:GRAVITATION
359742
Which of the following statement is correct regarding a geostationary satellite?
1 A geostationary satellite goes around the earth in east-west direction.
2 A geostationary satellite goes around the earth in west-east direction.
3 The time period of a geostationary satellite is 48 hours.
4 The angle between the equatorial plane and the orbital plane of geostationary satellite is \(90^{\circ}\).
Explanation:
A geostationary satellite goes around the earth in west-east direction. The time period a geostationary satellite is 24 hours. The angle between the equatorial plane and the orbital plane of geostationary satellite is \(0^{\circ}\).
PHXI08:GRAVITATION
359743
Assertion : Even when orbit of a satellite is elliptical. its plane of rotation passes through the centre of earth. Reason : According to law of conservation of angular momentum plane of rotation of satellite always remain same.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
Gravitational force \(F\) is a central force, meaning that \(F\) is function of \(r\) only (whether orbit is circular or elliptical). If ellipse, earth must lie at one of its foci. Gravitational force is attractive, internal and conservative. As there is no torque acting on the planet, its angular momentum must remain constant both in magnitude and direction. The plane of rotation shall have the center of the Earth. So correct option is (1).
PHXI08:GRAVITATION
359744
The orbital angular momentum of a satellite is \(L\), when it is revolving in a circular orbit at height \(h\) from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be
1 \(8\,L\)
2 \(4\,L\)
3 \(3\,L\)
4 \(9\,L\)
Explanation:
\(L=m v r\) \(v=\) Orbital velocity where, \(v=\sqrt{\dfrac{G m}{r}}\) \(\Rightarrow L \propto \sqrt{r} \because L \propto v r\) \(L^{\prime}=8 r+r=9 r\) or \(L^{\prime} \propto 3 \sqrt{r}\). All other parameters are constant then, \(L^{\prime}=3 L\)
