Acceleration Due to Gravity of the Earth
PHXI08:GRAVITATION

359593 Three particles of equal mass \(m\) are situated at the vertices of equilateral triangle of side \(\ell\). What should be the velocity of each particle, so that they move on a circular path?

1 \(\sqrt{\dfrac{G m}{\ell}}\)
2 \(\sqrt{\dfrac{G m}{2 \ell}}\)
3 \(\sqrt{\dfrac{G m}{3 \ell}}\)
4 \(\sqrt{\dfrac{2 G m}{\ell}}\)
PHXI08:GRAVITATION

359594 The acceleration due to gravity on the moon is one-sixth that of the earth. If the earth and moon are assumed to have the same density, the ratio of the radii of moon and earth will be

1 \(\dfrac{1}{(6)^{1 / 3}}\)
2 \(\dfrac{1}{6}\)
3 \(\dfrac{1}{(6)^{2 / 3}}\)
4 \(\dfrac{1}{36}\)
PHXI08:GRAVITATION

359595 The weight of a body on earth is denoted by \(W\) and the acceleration due to gravity is \(g\).
Newton's second law can be written as
\(F=\dfrac{W}{g} a\). The acceleration due to gravity on the moon is \(g_{1}\). What is the expression for Newton's law on the moon?

1 \(F=\dfrac{W}{g_{1}} a\)
2 \(F=\dfrac{W}{g} g_{1} a\)
3 \(F=\dfrac{W}{g} a\)
4 \(F=\dfrac{W}{g_{1}} g a\)
PHXI08:GRAVITATION

359596 A solid sphere of mass \(M\) and radius \(R\) is surrounded by a spherical shell of same mass \(M\) and radius 2\(R\) as shown. A small particle of mass \(m\) is released from rest from a height \(h( < < R)\) above the shell. There is a hole in the shell. In what time will it enter the hole at \(A\)
supporting img

1 \(\sqrt{\dfrac{2 h R^{2}}{G M}}\)
2 \(2 \sqrt{\dfrac{h R^{2}}{G M}}\)
3 \(\sqrt{\dfrac{h R^{2}}{G M}}\)
4 None of these
PHXI08:GRAVITATION

359597 The mass of a planet is \({\dfrac{1}{10}}\) th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

1 \({19.6 {~ms}^{-2}}\)
2 \({9.8 {~ms}^{-2}}\)
3 \({4.9 {~ms}^{-2}}\)
4 \({3.92 {~ms}^{-2}}\)
PHXI08:GRAVITATION

359593 Three particles of equal mass \(m\) are situated at the vertices of equilateral triangle of side \(\ell\). What should be the velocity of each particle, so that they move on a circular path?

1 \(\sqrt{\dfrac{G m}{\ell}}\)
2 \(\sqrt{\dfrac{G m}{2 \ell}}\)
3 \(\sqrt{\dfrac{G m}{3 \ell}}\)
4 \(\sqrt{\dfrac{2 G m}{\ell}}\)
PHXI08:GRAVITATION

359594 The acceleration due to gravity on the moon is one-sixth that of the earth. If the earth and moon are assumed to have the same density, the ratio of the radii of moon and earth will be

1 \(\dfrac{1}{(6)^{1 / 3}}\)
2 \(\dfrac{1}{6}\)
3 \(\dfrac{1}{(6)^{2 / 3}}\)
4 \(\dfrac{1}{36}\)
PHXI08:GRAVITATION

359595 The weight of a body on earth is denoted by \(W\) and the acceleration due to gravity is \(g\).
Newton's second law can be written as
\(F=\dfrac{W}{g} a\). The acceleration due to gravity on the moon is \(g_{1}\). What is the expression for Newton's law on the moon?

1 \(F=\dfrac{W}{g_{1}} a\)
2 \(F=\dfrac{W}{g} g_{1} a\)
3 \(F=\dfrac{W}{g} a\)
4 \(F=\dfrac{W}{g_{1}} g a\)
PHXI08:GRAVITATION

359596 A solid sphere of mass \(M\) and radius \(R\) is surrounded by a spherical shell of same mass \(M\) and radius 2\(R\) as shown. A small particle of mass \(m\) is released from rest from a height \(h( < < R)\) above the shell. There is a hole in the shell. In what time will it enter the hole at \(A\)
supporting img

1 \(\sqrt{\dfrac{2 h R^{2}}{G M}}\)
2 \(2 \sqrt{\dfrac{h R^{2}}{G M}}\)
3 \(\sqrt{\dfrac{h R^{2}}{G M}}\)
4 None of these
PHXI08:GRAVITATION

359597 The mass of a planet is \({\dfrac{1}{10}}\) th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

1 \({19.6 {~ms}^{-2}}\)
2 \({9.8 {~ms}^{-2}}\)
3 \({4.9 {~ms}^{-2}}\)
4 \({3.92 {~ms}^{-2}}\)
PHXI08:GRAVITATION

359593 Three particles of equal mass \(m\) are situated at the vertices of equilateral triangle of side \(\ell\). What should be the velocity of each particle, so that they move on a circular path?

1 \(\sqrt{\dfrac{G m}{\ell}}\)
2 \(\sqrt{\dfrac{G m}{2 \ell}}\)
3 \(\sqrt{\dfrac{G m}{3 \ell}}\)
4 \(\sqrt{\dfrac{2 G m}{\ell}}\)
PHXI08:GRAVITATION

359594 The acceleration due to gravity on the moon is one-sixth that of the earth. If the earth and moon are assumed to have the same density, the ratio of the radii of moon and earth will be

1 \(\dfrac{1}{(6)^{1 / 3}}\)
2 \(\dfrac{1}{6}\)
3 \(\dfrac{1}{(6)^{2 / 3}}\)
4 \(\dfrac{1}{36}\)
PHXI08:GRAVITATION

359595 The weight of a body on earth is denoted by \(W\) and the acceleration due to gravity is \(g\).
Newton's second law can be written as
\(F=\dfrac{W}{g} a\). The acceleration due to gravity on the moon is \(g_{1}\). What is the expression for Newton's law on the moon?

1 \(F=\dfrac{W}{g_{1}} a\)
2 \(F=\dfrac{W}{g} g_{1} a\)
3 \(F=\dfrac{W}{g} a\)
4 \(F=\dfrac{W}{g_{1}} g a\)
PHXI08:GRAVITATION

359596 A solid sphere of mass \(M\) and radius \(R\) is surrounded by a spherical shell of same mass \(M\) and radius 2\(R\) as shown. A small particle of mass \(m\) is released from rest from a height \(h( < < R)\) above the shell. There is a hole in the shell. In what time will it enter the hole at \(A\)
supporting img

1 \(\sqrt{\dfrac{2 h R^{2}}{G M}}\)
2 \(2 \sqrt{\dfrac{h R^{2}}{G M}}\)
3 \(\sqrt{\dfrac{h R^{2}}{G M}}\)
4 None of these
PHXI08:GRAVITATION

359597 The mass of a planet is \({\dfrac{1}{10}}\) th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

1 \({19.6 {~ms}^{-2}}\)
2 \({9.8 {~ms}^{-2}}\)
3 \({4.9 {~ms}^{-2}}\)
4 \({3.92 {~ms}^{-2}}\)
PHXI08:GRAVITATION

359593 Three particles of equal mass \(m\) are situated at the vertices of equilateral triangle of side \(\ell\). What should be the velocity of each particle, so that they move on a circular path?

1 \(\sqrt{\dfrac{G m}{\ell}}\)
2 \(\sqrt{\dfrac{G m}{2 \ell}}\)
3 \(\sqrt{\dfrac{G m}{3 \ell}}\)
4 \(\sqrt{\dfrac{2 G m}{\ell}}\)
PHXI08:GRAVITATION

359594 The acceleration due to gravity on the moon is one-sixth that of the earth. If the earth and moon are assumed to have the same density, the ratio of the radii of moon and earth will be

1 \(\dfrac{1}{(6)^{1 / 3}}\)
2 \(\dfrac{1}{6}\)
3 \(\dfrac{1}{(6)^{2 / 3}}\)
4 \(\dfrac{1}{36}\)
PHXI08:GRAVITATION

359595 The weight of a body on earth is denoted by \(W\) and the acceleration due to gravity is \(g\).
Newton's second law can be written as
\(F=\dfrac{W}{g} a\). The acceleration due to gravity on the moon is \(g_{1}\). What is the expression for Newton's law on the moon?

1 \(F=\dfrac{W}{g_{1}} a\)
2 \(F=\dfrac{W}{g} g_{1} a\)
3 \(F=\dfrac{W}{g} a\)
4 \(F=\dfrac{W}{g_{1}} g a\)
PHXI08:GRAVITATION

359596 A solid sphere of mass \(M\) and radius \(R\) is surrounded by a spherical shell of same mass \(M\) and radius 2\(R\) as shown. A small particle of mass \(m\) is released from rest from a height \(h( < < R)\) above the shell. There is a hole in the shell. In what time will it enter the hole at \(A\)
supporting img

1 \(\sqrt{\dfrac{2 h R^{2}}{G M}}\)
2 \(2 \sqrt{\dfrac{h R^{2}}{G M}}\)
3 \(\sqrt{\dfrac{h R^{2}}{G M}}\)
4 None of these
PHXI08:GRAVITATION

359597 The mass of a planet is \({\dfrac{1}{10}}\) th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

1 \({19.6 {~ms}^{-2}}\)
2 \({9.8 {~ms}^{-2}}\)
3 \({4.9 {~ms}^{-2}}\)
4 \({3.92 {~ms}^{-2}}\)
PHXI08:GRAVITATION

359593 Three particles of equal mass \(m\) are situated at the vertices of equilateral triangle of side \(\ell\). What should be the velocity of each particle, so that they move on a circular path?

1 \(\sqrt{\dfrac{G m}{\ell}}\)
2 \(\sqrt{\dfrac{G m}{2 \ell}}\)
3 \(\sqrt{\dfrac{G m}{3 \ell}}\)
4 \(\sqrt{\dfrac{2 G m}{\ell}}\)
PHXI08:GRAVITATION

359594 The acceleration due to gravity on the moon is one-sixth that of the earth. If the earth and moon are assumed to have the same density, the ratio of the radii of moon and earth will be

1 \(\dfrac{1}{(6)^{1 / 3}}\)
2 \(\dfrac{1}{6}\)
3 \(\dfrac{1}{(6)^{2 / 3}}\)
4 \(\dfrac{1}{36}\)
PHXI08:GRAVITATION

359595 The weight of a body on earth is denoted by \(W\) and the acceleration due to gravity is \(g\).
Newton's second law can be written as
\(F=\dfrac{W}{g} a\). The acceleration due to gravity on the moon is \(g_{1}\). What is the expression for Newton's law on the moon?

1 \(F=\dfrac{W}{g_{1}} a\)
2 \(F=\dfrac{W}{g} g_{1} a\)
3 \(F=\dfrac{W}{g} a\)
4 \(F=\dfrac{W}{g_{1}} g a\)
PHXI08:GRAVITATION

359596 A solid sphere of mass \(M\) and radius \(R\) is surrounded by a spherical shell of same mass \(M\) and radius 2\(R\) as shown. A small particle of mass \(m\) is released from rest from a height \(h( < < R)\) above the shell. There is a hole in the shell. In what time will it enter the hole at \(A\)
supporting img

1 \(\sqrt{\dfrac{2 h R^{2}}{G M}}\)
2 \(2 \sqrt{\dfrac{h R^{2}}{G M}}\)
3 \(\sqrt{\dfrac{h R^{2}}{G M}}\)
4 None of these
PHXI08:GRAVITATION

359597 The mass of a planet is \({\dfrac{1}{10}}\) th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

1 \({19.6 {~ms}^{-2}}\)
2 \({9.8 {~ms}^{-2}}\)
3 \({4.9 {~ms}^{-2}}\)
4 \({3.92 {~ms}^{-2}}\)