Gravitational Potential
PHXI08:GRAVITATION

359871 From a solid sphere of mass \(M\) and radius \(R\), a spherical portion of radius \(\dfrac{R}{2}\) is removed, as shown in the figure. Taking gravitational potential \(V=0\) at \(r=\infty\), the potential at the centre of the cavity thus formed is
(\(G=\) Gravitational constant)
supporting img

1 \(\dfrac{-2 G M}{R}\)
2 \(\dfrac{-2 G M}{3 R}\)
3 \(\dfrac{-G M}{2 R}\)
4 \(\dfrac{-G M}{R}\)
PHXI08:GRAVITATION

359872 A particle of mass \(M\) is situated at the centre of a spherical shell of same mass and radius \(a\). The gravitational potential at a point situated at \(a / 2\) distance from the centre, will be

1 \(-\dfrac{2 G M}{a}\)
2 \(-\dfrac{4 G M}{a}\)
3 \(-\dfrac{G M}{a}\)
4 \(-\dfrac{3 G M}{a}\)
PHXI08:GRAVITATION

359873 Two bodies of mass \(m\) and \(9 m\) are placed at a distance \(R\). The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ( \(G=\) gravitational constant):

1 \(-\dfrac{12 G m}{R}\)
2 \(-\dfrac{16 G m}{R}\)
3 \(-\dfrac{20 G m}{R}\)
4 \(-\dfrac{8 G m}{R}\)
PHXI08:GRAVITATION

359874 If \(V\) is the gravitational potential due to sphere of uniform density on it's surface, then its value at the centre of sphere will be

1 \(V / 2\)
2 \(3\,V/2\)
3 \(V\)
4 \({4{\rm{ }}/{\rm{ }}3\,V}\)
PHXI08:GRAVITATION

359871 From a solid sphere of mass \(M\) and radius \(R\), a spherical portion of radius \(\dfrac{R}{2}\) is removed, as shown in the figure. Taking gravitational potential \(V=0\) at \(r=\infty\), the potential at the centre of the cavity thus formed is
(\(G=\) Gravitational constant)
supporting img

1 \(\dfrac{-2 G M}{R}\)
2 \(\dfrac{-2 G M}{3 R}\)
3 \(\dfrac{-G M}{2 R}\)
4 \(\dfrac{-G M}{R}\)
PHXI08:GRAVITATION

359872 A particle of mass \(M\) is situated at the centre of a spherical shell of same mass and radius \(a\). The gravitational potential at a point situated at \(a / 2\) distance from the centre, will be

1 \(-\dfrac{2 G M}{a}\)
2 \(-\dfrac{4 G M}{a}\)
3 \(-\dfrac{G M}{a}\)
4 \(-\dfrac{3 G M}{a}\)
PHXI08:GRAVITATION

359873 Two bodies of mass \(m\) and \(9 m\) are placed at a distance \(R\). The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ( \(G=\) gravitational constant):

1 \(-\dfrac{12 G m}{R}\)
2 \(-\dfrac{16 G m}{R}\)
3 \(-\dfrac{20 G m}{R}\)
4 \(-\dfrac{8 G m}{R}\)
PHXI08:GRAVITATION

359874 If \(V\) is the gravitational potential due to sphere of uniform density on it's surface, then its value at the centre of sphere will be

1 \(V / 2\)
2 \(3\,V/2\)
3 \(V\)
4 \({4{\rm{ }}/{\rm{ }}3\,V}\)
PHXI08:GRAVITATION

359871 From a solid sphere of mass \(M\) and radius \(R\), a spherical portion of radius \(\dfrac{R}{2}\) is removed, as shown in the figure. Taking gravitational potential \(V=0\) at \(r=\infty\), the potential at the centre of the cavity thus formed is
(\(G=\) Gravitational constant)
supporting img

1 \(\dfrac{-2 G M}{R}\)
2 \(\dfrac{-2 G M}{3 R}\)
3 \(\dfrac{-G M}{2 R}\)
4 \(\dfrac{-G M}{R}\)
PHXI08:GRAVITATION

359872 A particle of mass \(M\) is situated at the centre of a spherical shell of same mass and radius \(a\). The gravitational potential at a point situated at \(a / 2\) distance from the centre, will be

1 \(-\dfrac{2 G M}{a}\)
2 \(-\dfrac{4 G M}{a}\)
3 \(-\dfrac{G M}{a}\)
4 \(-\dfrac{3 G M}{a}\)
PHXI08:GRAVITATION

359873 Two bodies of mass \(m\) and \(9 m\) are placed at a distance \(R\). The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ( \(G=\) gravitational constant):

1 \(-\dfrac{12 G m}{R}\)
2 \(-\dfrac{16 G m}{R}\)
3 \(-\dfrac{20 G m}{R}\)
4 \(-\dfrac{8 G m}{R}\)
PHXI08:GRAVITATION

359874 If \(V\) is the gravitational potential due to sphere of uniform density on it's surface, then its value at the centre of sphere will be

1 \(V / 2\)
2 \(3\,V/2\)
3 \(V\)
4 \({4{\rm{ }}/{\rm{ }}3\,V}\)
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PHXI08:GRAVITATION

359871 From a solid sphere of mass \(M\) and radius \(R\), a spherical portion of radius \(\dfrac{R}{2}\) is removed, as shown in the figure. Taking gravitational potential \(V=0\) at \(r=\infty\), the potential at the centre of the cavity thus formed is
(\(G=\) Gravitational constant)
supporting img

1 \(\dfrac{-2 G M}{R}\)
2 \(\dfrac{-2 G M}{3 R}\)
3 \(\dfrac{-G M}{2 R}\)
4 \(\dfrac{-G M}{R}\)
PHXI08:GRAVITATION

359872 A particle of mass \(M\) is situated at the centre of a spherical shell of same mass and radius \(a\). The gravitational potential at a point situated at \(a / 2\) distance from the centre, will be

1 \(-\dfrac{2 G M}{a}\)
2 \(-\dfrac{4 G M}{a}\)
3 \(-\dfrac{G M}{a}\)
4 \(-\dfrac{3 G M}{a}\)
PHXI08:GRAVITATION

359873 Two bodies of mass \(m\) and \(9 m\) are placed at a distance \(R\). The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be ( \(G=\) gravitational constant):

1 \(-\dfrac{12 G m}{R}\)
2 \(-\dfrac{16 G m}{R}\)
3 \(-\dfrac{20 G m}{R}\)
4 \(-\dfrac{8 G m}{R}\)
PHXI08:GRAVITATION

359874 If \(V\) is the gravitational potential due to sphere of uniform density on it's surface, then its value at the centre of sphere will be

1 \(V / 2\)
2 \(3\,V/2\)
3 \(V\)
4 \({4{\rm{ }}/{\rm{ }}3\,V}\)