Suppose a straight tube could be drilled right through the Earth, modelled as a uniform sphere of radius R and total mass M. A ball of unit mass is dropped into the tube at the floor of the Earth.
Suppose a straight tube could be drilled right through the Earth, modelled as a uniform sphere of radius R and total mass M. A ball of unit mass is dropped into the tube at the floor of the Earth.
A physique of unit mass inside a uniform sphere at a distance r from its centre O experiences a gravitational attraction in direction of the centre ofwhere G is the gravitational fixed and Mr is the mass of materials inside the sphere of radius r.
(In different phrases it’s as if the physique had been on the floor of a sphere of radius r, all the matter farther from the centre than r may have no web gravitational impact on the physique.)
Suppose a straight tube could be drilled right through the Earth, modelled as a uniform sphere of radius R and total mass M. A ball of unit mass is dropped into the tube at the floor of the Earth.
i) Work out the mass of a sphere of the Earth of radius r, in phrases of R, M and r.
ii) Write down an expression for the gravitational power on the ball when at a distance r from the centre.
iii) Therefore present that the ball will oscillate with easy harmonic movement with an amplitude equal to the radius of the Earth. Decide the interval.
Assume that a straight tube, described as a homogeneous sphere of radius R and total mass M, could be dug immediately through the Earth. A unit mass ball is put into the tube close to the Earth’s floor.
Assume that a straight tube, described as a homogeneous sphere of radius R and total mass M, could be dug immediately through the Earth. A unit mass ball is put into the tube close to the Earth’s floor.
A physique with unit mass positioned at r from the middle of a uniform sphere. The place G is the gravitational fixed and Mr is the mass of materials inside the sphere of radius r, O experiences a gravitational attraction in direction of the middle of.
(To place it one other means, it
