359749
Statement A : Electrical force is experienced by charged particles only. Statement B : There is no gravitational force on the satellite.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Gravitational force on the person in satellite is not zero, but normal reaction of the satellite on the person is zero.
PHXI08:GRAVITATION
359750
Suppose the gravitational force varies inversely as the \(n^{\text {th }}\) power of distance. Then the time period of a planet in circular orbit of radius \(R\) around the sun will be proportional to
359751
An earth satellite is moved from one stable circular orbit to another larger and stable circular orbit. The following quantities increase for the satellite as a result of this change
1 Gravitational potential energy
2 Angular vleocity
3 Linear orbital velocity
4 Centripetal acceleration
Explanation:
When a satellite is in stable orbit then its time period is \(\begin{gathered}T=2 \pi \sqrt{\dfrac{r^{3}}{G M}}=\dfrac{2 \pi}{\omega} \\\omega=\sqrt{\dfrac{G M}{r^{3}}} \Rightarrow \omega \alpha \sqrt{\dfrac{1}{r^{3}}} \\v_{0}=\sqrt{\dfrac{G M}{r}} \Rightarrow v_{0} \alpha \sqrt{\dfrac{1}{r}} \\U=\dfrac{-G M m}{r} \text { As } r \text { increases } U \text { also increases }\end{gathered}\) The centripetal acceleration is \(a_{r}=\dfrac{v_{0}^{2}}{r}=\dfrac{G M}{r^{2}} \Rightarrow a_{r} \alpha \dfrac{1}{r}\)
PHXI08:GRAVITATION
359752
Two satellites \(A\) and \(B\) go round a planet in circular orbits having radii \(4 R\) and \(R\) respectively. If the speed of \(A\) is \(3 v\), the speed of \(B\) will be
1 \(12 v\)
2 \(\dfrac{4}{3} v\)
3 \(6 v\)
4 \(3 v\)
Explanation:
Orbital speed is given by \(v_{0}=\sqrt{\dfrac{G M}{R}}\) where \(r=\) radius of orbit \(v_{\text {orbital }}=\sqrt{\dfrac{G M}{R}}\) \(v_{A}=3 v=\sqrt{\dfrac{G M}{4 R}}\) \(\quad \;(1)\) and \(v_{B}=\sqrt{\dfrac{G M}{R}}\) \(\quad \;(2)\) From eq (1) and (2) \(\dfrac{3 v}{v_{B}}=\dfrac{1}{2} \quad \therefore v_{B}=6 v\)
359749
Statement A : Electrical force is experienced by charged particles only. Statement B : There is no gravitational force on the satellite.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Gravitational force on the person in satellite is not zero, but normal reaction of the satellite on the person is zero.
PHXI08:GRAVITATION
359750
Suppose the gravitational force varies inversely as the \(n^{\text {th }}\) power of distance. Then the time period of a planet in circular orbit of radius \(R\) around the sun will be proportional to
359751
An earth satellite is moved from one stable circular orbit to another larger and stable circular orbit. The following quantities increase for the satellite as a result of this change
1 Gravitational potential energy
2 Angular vleocity
3 Linear orbital velocity
4 Centripetal acceleration
Explanation:
When a satellite is in stable orbit then its time period is \(\begin{gathered}T=2 \pi \sqrt{\dfrac{r^{3}}{G M}}=\dfrac{2 \pi}{\omega} \\\omega=\sqrt{\dfrac{G M}{r^{3}}} \Rightarrow \omega \alpha \sqrt{\dfrac{1}{r^{3}}} \\v_{0}=\sqrt{\dfrac{G M}{r}} \Rightarrow v_{0} \alpha \sqrt{\dfrac{1}{r}} \\U=\dfrac{-G M m}{r} \text { As } r \text { increases } U \text { also increases }\end{gathered}\) The centripetal acceleration is \(a_{r}=\dfrac{v_{0}^{2}}{r}=\dfrac{G M}{r^{2}} \Rightarrow a_{r} \alpha \dfrac{1}{r}\)
PHXI08:GRAVITATION
359752
Two satellites \(A\) and \(B\) go round a planet in circular orbits having radii \(4 R\) and \(R\) respectively. If the speed of \(A\) is \(3 v\), the speed of \(B\) will be
1 \(12 v\)
2 \(\dfrac{4}{3} v\)
3 \(6 v\)
4 \(3 v\)
Explanation:
Orbital speed is given by \(v_{0}=\sqrt{\dfrac{G M}{R}}\) where \(r=\) radius of orbit \(v_{\text {orbital }}=\sqrt{\dfrac{G M}{R}}\) \(v_{A}=3 v=\sqrt{\dfrac{G M}{4 R}}\) \(\quad \;(1)\) and \(v_{B}=\sqrt{\dfrac{G M}{R}}\) \(\quad \;(2)\) From eq (1) and (2) \(\dfrac{3 v}{v_{B}}=\dfrac{1}{2} \quad \therefore v_{B}=6 v\)
359749
Statement A : Electrical force is experienced by charged particles only. Statement B : There is no gravitational force on the satellite.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Gravitational force on the person in satellite is not zero, but normal reaction of the satellite on the person is zero.
PHXI08:GRAVITATION
359750
Suppose the gravitational force varies inversely as the \(n^{\text {th }}\) power of distance. Then the time period of a planet in circular orbit of radius \(R\) around the sun will be proportional to
359751
An earth satellite is moved from one stable circular orbit to another larger and stable circular orbit. The following quantities increase for the satellite as a result of this change
1 Gravitational potential energy
2 Angular vleocity
3 Linear orbital velocity
4 Centripetal acceleration
Explanation:
When a satellite is in stable orbit then its time period is \(\begin{gathered}T=2 \pi \sqrt{\dfrac{r^{3}}{G M}}=\dfrac{2 \pi}{\omega} \\\omega=\sqrt{\dfrac{G M}{r^{3}}} \Rightarrow \omega \alpha \sqrt{\dfrac{1}{r^{3}}} \\v_{0}=\sqrt{\dfrac{G M}{r}} \Rightarrow v_{0} \alpha \sqrt{\dfrac{1}{r}} \\U=\dfrac{-G M m}{r} \text { As } r \text { increases } U \text { also increases }\end{gathered}\) The centripetal acceleration is \(a_{r}=\dfrac{v_{0}^{2}}{r}=\dfrac{G M}{r^{2}} \Rightarrow a_{r} \alpha \dfrac{1}{r}\)
PHXI08:GRAVITATION
359752
Two satellites \(A\) and \(B\) go round a planet in circular orbits having radii \(4 R\) and \(R\) respectively. If the speed of \(A\) is \(3 v\), the speed of \(B\) will be
1 \(12 v\)
2 \(\dfrac{4}{3} v\)
3 \(6 v\)
4 \(3 v\)
Explanation:
Orbital speed is given by \(v_{0}=\sqrt{\dfrac{G M}{R}}\) where \(r=\) radius of orbit \(v_{\text {orbital }}=\sqrt{\dfrac{G M}{R}}\) \(v_{A}=3 v=\sqrt{\dfrac{G M}{4 R}}\) \(\quad \;(1)\) and \(v_{B}=\sqrt{\dfrac{G M}{R}}\) \(\quad \;(2)\) From eq (1) and (2) \(\dfrac{3 v}{v_{B}}=\dfrac{1}{2} \quad \therefore v_{B}=6 v\)
359749
Statement A : Electrical force is experienced by charged particles only. Statement B : There is no gravitational force on the satellite.
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both statements are correct.
4 Both Statements are incorrect.
Explanation:
Gravitational force on the person in satellite is not zero, but normal reaction of the satellite on the person is zero.
PHXI08:GRAVITATION
359750
Suppose the gravitational force varies inversely as the \(n^{\text {th }}\) power of distance. Then the time period of a planet in circular orbit of radius \(R\) around the sun will be proportional to
359751
An earth satellite is moved from one stable circular orbit to another larger and stable circular orbit. The following quantities increase for the satellite as a result of this change
1 Gravitational potential energy
2 Angular vleocity
3 Linear orbital velocity
4 Centripetal acceleration
Explanation:
When a satellite is in stable orbit then its time period is \(\begin{gathered}T=2 \pi \sqrt{\dfrac{r^{3}}{G M}}=\dfrac{2 \pi}{\omega} \\\omega=\sqrt{\dfrac{G M}{r^{3}}} \Rightarrow \omega \alpha \sqrt{\dfrac{1}{r^{3}}} \\v_{0}=\sqrt{\dfrac{G M}{r}} \Rightarrow v_{0} \alpha \sqrt{\dfrac{1}{r}} \\U=\dfrac{-G M m}{r} \text { As } r \text { increases } U \text { also increases }\end{gathered}\) The centripetal acceleration is \(a_{r}=\dfrac{v_{0}^{2}}{r}=\dfrac{G M}{r^{2}} \Rightarrow a_{r} \alpha \dfrac{1}{r}\)
PHXI08:GRAVITATION
359752
Two satellites \(A\) and \(B\) go round a planet in circular orbits having radii \(4 R\) and \(R\) respectively. If the speed of \(A\) is \(3 v\), the speed of \(B\) will be
1 \(12 v\)
2 \(\dfrac{4}{3} v\)
3 \(6 v\)
4 \(3 v\)
Explanation:
Orbital speed is given by \(v_{0}=\sqrt{\dfrac{G M}{R}}\) where \(r=\) radius of orbit \(v_{\text {orbital }}=\sqrt{\dfrac{G M}{R}}\) \(v_{A}=3 v=\sqrt{\dfrac{G M}{4 R}}\) \(\quad \;(1)\) and \(v_{B}=\sqrt{\dfrac{G M}{R}}\) \(\quad \;(2)\) From eq (1) and (2) \(\dfrac{3 v}{v_{B}}=\dfrac{1}{2} \quad \therefore v_{B}=6 v\)
