359946
A satellite of mass \(m\) is revolving in circular orbit of radius \(r\) around the earth. Its angular momentum w.r.t the centre of its orbit is (\(M=\) mass of earth, \(G=\) universal gravitational constant)
1 \((G M m r)^{1 / 2}\)
2 \(\left(G M m^{2} r\right)^{1 / 2}\)
3 \(\left(G M m^{2} r^{2}\right)^{1 / 2}\)
4 \(\left(G M^{2} m^{2} r^{2}\right)^{1 / 2}\)
Explanation:
Orbital speed of the statellite,\(v=\sqrt{\dfrac{G M}{r}}\) Angular momentum of the statellite, \(L=m v r=m r \times \sqrt{\dfrac{G M}{r}}=\left(G M m^{2} r\right)^{1 / 2}\)
MHTCET - 2015
PHXI08:GRAVITATION
359947
If the angular momentum of a planet of mass \(m\), moving around the Sun in a circular orbit is \(L\), about the centre of the Sun, its areal velocity is
1 \(\frac{{4\;L}}{{\;m}}\)
2 \(\dfrac{L}{2 m}\)
3 \(\dfrac{2 L}{m}\)
4 \(\dfrac{L}{m}\)
Explanation:
The angular momentum of the planet about the sun is \(\vec L = \vec r \times m\vec r\) \(L = rm\frac{{\Delta s}}{{\Delta t}} = \frac{m}{{\Delta t}}(r\Delta s)\) \(L = \frac{m}{{\Delta t}}(2\Delta A) \Rightarrow \frac{{\Delta A}}{{\Delta t}} = \frac{L}{{2\;m}}\) Where \({\Delta A}\) is the area sweep by the planet in time \({\Delta t}\).
JEE - 2019
PHXI08:GRAVITATION
359948
When a planet revolves around the Sun, in general, for the planet
1 kinetic and potential energy of the planet are constant.
2 angular momentum about the Sun and aerial velocity of the planet are constant.
3 linear momentum and linear velocity are constant.
4 linear momentum and aerial velocity are constant.
359946
A satellite of mass \(m\) is revolving in circular orbit of radius \(r\) around the earth. Its angular momentum w.r.t the centre of its orbit is (\(M=\) mass of earth, \(G=\) universal gravitational constant)
1 \((G M m r)^{1 / 2}\)
2 \(\left(G M m^{2} r\right)^{1 / 2}\)
3 \(\left(G M m^{2} r^{2}\right)^{1 / 2}\)
4 \(\left(G M^{2} m^{2} r^{2}\right)^{1 / 2}\)
Explanation:
Orbital speed of the statellite,\(v=\sqrt{\dfrac{G M}{r}}\) Angular momentum of the statellite, \(L=m v r=m r \times \sqrt{\dfrac{G M}{r}}=\left(G M m^{2} r\right)^{1 / 2}\)
MHTCET - 2015
PHXI08:GRAVITATION
359947
If the angular momentum of a planet of mass \(m\), moving around the Sun in a circular orbit is \(L\), about the centre of the Sun, its areal velocity is
1 \(\frac{{4\;L}}{{\;m}}\)
2 \(\dfrac{L}{2 m}\)
3 \(\dfrac{2 L}{m}\)
4 \(\dfrac{L}{m}\)
Explanation:
The angular momentum of the planet about the sun is \(\vec L = \vec r \times m\vec r\) \(L = rm\frac{{\Delta s}}{{\Delta t}} = \frac{m}{{\Delta t}}(r\Delta s)\) \(L = \frac{m}{{\Delta t}}(2\Delta A) \Rightarrow \frac{{\Delta A}}{{\Delta t}} = \frac{L}{{2\;m}}\) Where \({\Delta A}\) is the area sweep by the planet in time \({\Delta t}\).
JEE - 2019
PHXI08:GRAVITATION
359948
When a planet revolves around the Sun, in general, for the planet
1 kinetic and potential energy of the planet are constant.
2 angular momentum about the Sun and aerial velocity of the planet are constant.
3 linear momentum and linear velocity are constant.
4 linear momentum and aerial velocity are constant.
359946
A satellite of mass \(m\) is revolving in circular orbit of radius \(r\) around the earth. Its angular momentum w.r.t the centre of its orbit is (\(M=\) mass of earth, \(G=\) universal gravitational constant)
1 \((G M m r)^{1 / 2}\)
2 \(\left(G M m^{2} r\right)^{1 / 2}\)
3 \(\left(G M m^{2} r^{2}\right)^{1 / 2}\)
4 \(\left(G M^{2} m^{2} r^{2}\right)^{1 / 2}\)
Explanation:
Orbital speed of the statellite,\(v=\sqrt{\dfrac{G M}{r}}\) Angular momentum of the statellite, \(L=m v r=m r \times \sqrt{\dfrac{G M}{r}}=\left(G M m^{2} r\right)^{1 / 2}\)
MHTCET - 2015
PHXI08:GRAVITATION
359947
If the angular momentum of a planet of mass \(m\), moving around the Sun in a circular orbit is \(L\), about the centre of the Sun, its areal velocity is
1 \(\frac{{4\;L}}{{\;m}}\)
2 \(\dfrac{L}{2 m}\)
3 \(\dfrac{2 L}{m}\)
4 \(\dfrac{L}{m}\)
Explanation:
The angular momentum of the planet about the sun is \(\vec L = \vec r \times m\vec r\) \(L = rm\frac{{\Delta s}}{{\Delta t}} = \frac{m}{{\Delta t}}(r\Delta s)\) \(L = \frac{m}{{\Delta t}}(2\Delta A) \Rightarrow \frac{{\Delta A}}{{\Delta t}} = \frac{L}{{2\;m}}\) Where \({\Delta A}\) is the area sweep by the planet in time \({\Delta t}\).
JEE - 2019
PHXI08:GRAVITATION
359948
When a planet revolves around the Sun, in general, for the planet
1 kinetic and potential energy of the planet are constant.
2 angular momentum about the Sun and aerial velocity of the planet are constant.
3 linear momentum and linear velocity are constant.
4 linear momentum and aerial velocity are constant.
NEET Test Series from KOTA - 10 Papers In MS WORD
WhatsApp Here
PHXI08:GRAVITATION
359946
A satellite of mass \(m\) is revolving in circular orbit of radius \(r\) around the earth. Its angular momentum w.r.t the centre of its orbit is (\(M=\) mass of earth, \(G=\) universal gravitational constant)
1 \((G M m r)^{1 / 2}\)
2 \(\left(G M m^{2} r\right)^{1 / 2}\)
3 \(\left(G M m^{2} r^{2}\right)^{1 / 2}\)
4 \(\left(G M^{2} m^{2} r^{2}\right)^{1 / 2}\)
Explanation:
Orbital speed of the statellite,\(v=\sqrt{\dfrac{G M}{r}}\) Angular momentum of the statellite, \(L=m v r=m r \times \sqrt{\dfrac{G M}{r}}=\left(G M m^{2} r\right)^{1 / 2}\)
MHTCET - 2015
PHXI08:GRAVITATION
359947
If the angular momentum of a planet of mass \(m\), moving around the Sun in a circular orbit is \(L\), about the centre of the Sun, its areal velocity is
1 \(\frac{{4\;L}}{{\;m}}\)
2 \(\dfrac{L}{2 m}\)
3 \(\dfrac{2 L}{m}\)
4 \(\dfrac{L}{m}\)
Explanation:
The angular momentum of the planet about the sun is \(\vec L = \vec r \times m\vec r\) \(L = rm\frac{{\Delta s}}{{\Delta t}} = \frac{m}{{\Delta t}}(r\Delta s)\) \(L = \frac{m}{{\Delta t}}(2\Delta A) \Rightarrow \frac{{\Delta A}}{{\Delta t}} = \frac{L}{{2\;m}}\) Where \({\Delta A}\) is the area sweep by the planet in time \({\Delta t}\).
JEE - 2019
PHXI08:GRAVITATION
359948
When a planet revolves around the Sun, in general, for the planet
1 kinetic and potential energy of the planet are constant.
2 angular momentum about the Sun and aerial velocity of the planet are constant.
3 linear momentum and linear velocity are constant.
4 linear momentum and aerial velocity are constant.
