Acceleration Due to Gravity of the Earth
PHXI08:GRAVITATION

359658 An object is placed at a distance of \(R / 2\) from the centre of earth. Knowing mass is distributed uniformly, acceleration of that object due to gravity at that point is: ( \(g=\) acceleration due to gravity on the surface of earth and \(R\) is the radius of earth)

1 \(g\)
2 \(2\,g\)
3 \(g / 2\)
4 None of these
PHXI08:GRAVITATION

359659 The ratio of the accelerations due to gravity at the bottom of a deep mine and that on the surface of the earth is 978 / 980 . Find the depth of the mine, if the density of the earth is uniform throughout and the radius of the earth is 6300 \(\mathrm{km}\).

1 \(12.86 \mathrm{~km}\)
2 \(13.0 \mathrm{~km}\)
3 \(25.38 \mathrm{~km}\)
4 \(90.9 \mathrm{~km}\)
PHXI08:GRAVITATION

359660 Assuming the earth to be a sphere of uniform mass density, how much would body weight half way down to the centre of earth if it weighted 250 \(N\) on the surface?

1 225 \(N\)
2 325 \(N\)
3 100 \(N\)
4 125 \(N\)
PHXI08:GRAVITATION

359661 Scientists dig a well of depth \(\dfrac{R}{5}\) on earth and lower a wire of the same length and of linear mass density \({10^{ - 3}}kg{m^{ - 1}}\) into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (radius of earth \( = 6 \times {10^6}\;m\), acceleration due to gravity of earth is \(10\;m{s^{ - 2}}\))

1 10.8 \(KN\)
2 108 \(N\)
3 150 \(N\)
4 120 \(N\)
PHXI08:GRAVITATION

359658 An object is placed at a distance of \(R / 2\) from the centre of earth. Knowing mass is distributed uniformly, acceleration of that object due to gravity at that point is: ( \(g=\) acceleration due to gravity on the surface of earth and \(R\) is the radius of earth)

1 \(g\)
2 \(2\,g\)
3 \(g / 2\)
4 None of these
PHXI08:GRAVITATION

359659 The ratio of the accelerations due to gravity at the bottom of a deep mine and that on the surface of the earth is 978 / 980 . Find the depth of the mine, if the density of the earth is uniform throughout and the radius of the earth is 6300 \(\mathrm{km}\).

1 \(12.86 \mathrm{~km}\)
2 \(13.0 \mathrm{~km}\)
3 \(25.38 \mathrm{~km}\)
4 \(90.9 \mathrm{~km}\)
PHXI08:GRAVITATION

359660 Assuming the earth to be a sphere of uniform mass density, how much would body weight half way down to the centre of earth if it weighted 250 \(N\) on the surface?

1 225 \(N\)
2 325 \(N\)
3 100 \(N\)
4 125 \(N\)
PHXI08:GRAVITATION

359661 Scientists dig a well of depth \(\dfrac{R}{5}\) on earth and lower a wire of the same length and of linear mass density \({10^{ - 3}}kg{m^{ - 1}}\) into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (radius of earth \( = 6 \times {10^6}\;m\), acceleration due to gravity of earth is \(10\;m{s^{ - 2}}\))

1 10.8 \(KN\)
2 108 \(N\)
3 150 \(N\)
4 120 \(N\)
PHXI08:GRAVITATION

359658 An object is placed at a distance of \(R / 2\) from the centre of earth. Knowing mass is distributed uniformly, acceleration of that object due to gravity at that point is: ( \(g=\) acceleration due to gravity on the surface of earth and \(R\) is the radius of earth)

1 \(g\)
2 \(2\,g\)
3 \(g / 2\)
4 None of these
PHXI08:GRAVITATION

359659 The ratio of the accelerations due to gravity at the bottom of a deep mine and that on the surface of the earth is 978 / 980 . Find the depth of the mine, if the density of the earth is uniform throughout and the radius of the earth is 6300 \(\mathrm{km}\).

1 \(12.86 \mathrm{~km}\)
2 \(13.0 \mathrm{~km}\)
3 \(25.38 \mathrm{~km}\)
4 \(90.9 \mathrm{~km}\)
PHXI08:GRAVITATION

359660 Assuming the earth to be a sphere of uniform mass density, how much would body weight half way down to the centre of earth if it weighted 250 \(N\) on the surface?

1 225 \(N\)
2 325 \(N\)
3 100 \(N\)
4 125 \(N\)
PHXI08:GRAVITATION

359661 Scientists dig a well of depth \(\dfrac{R}{5}\) on earth and lower a wire of the same length and of linear mass density \({10^{ - 3}}kg{m^{ - 1}}\) into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (radius of earth \( = 6 \times {10^6}\;m\), acceleration due to gravity of earth is \(10\;m{s^{ - 2}}\))

1 10.8 \(KN\)
2 108 \(N\)
3 150 \(N\)
4 120 \(N\)
PHXI08:GRAVITATION

359658 An object is placed at a distance of \(R / 2\) from the centre of earth. Knowing mass is distributed uniformly, acceleration of that object due to gravity at that point is: ( \(g=\) acceleration due to gravity on the surface of earth and \(R\) is the radius of earth)

1 \(g\)
2 \(2\,g\)
3 \(g / 2\)
4 None of these
PHXI08:GRAVITATION

359659 The ratio of the accelerations due to gravity at the bottom of a deep mine and that on the surface of the earth is 978 / 980 . Find the depth of the mine, if the density of the earth is uniform throughout and the radius of the earth is 6300 \(\mathrm{km}\).

1 \(12.86 \mathrm{~km}\)
2 \(13.0 \mathrm{~km}\)
3 \(25.38 \mathrm{~km}\)
4 \(90.9 \mathrm{~km}\)
PHXI08:GRAVITATION

359660 Assuming the earth to be a sphere of uniform mass density, how much would body weight half way down to the centre of earth if it weighted 250 \(N\) on the surface?

1 225 \(N\)
2 325 \(N\)
3 100 \(N\)
4 125 \(N\)
PHXI08:GRAVITATION

359661 Scientists dig a well of depth \(\dfrac{R}{5}\) on earth and lower a wire of the same length and of linear mass density \({10^{ - 3}}kg{m^{ - 1}}\) into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (radius of earth \( = 6 \times {10^6}\;m\), acceleration due to gravity of earth is \(10\;m{s^{ - 2}}\))

1 10.8 \(KN\)
2 108 \(N\)
3 150 \(N\)
4 120 \(N\)