# Metallic and glass sphere of same size released at a height

This question was in my exam today :

A metallic and glass sphere of same size were dropped at same height. Which sphere would hit the ground first and why?

I have thought about several things and cannot come to conclusion. An emf will be developed as electrons will move due to earth's magnetic field. So we have a charged sphere? What now? Magnetic force will be perpendicular to velocity hence no work done by it.

If only someone could just point me in the right direction.

• Unless the two are also the same weight, the question is unanswerable. – Hot Licks Jan 31 '15 at 4:36
• @HotLicks Even if the 2 objects have the same mass, it would be very difficult to answer since it doesn't indicate if we should account for the magnetic influence on the metallic sphere. – LDC3 Jan 31 '15 at 5:05
• @LDC3 - True, we would also need to know the magnetic properties of the metallic sphere. If the metal used has no magnetic properties (ferromagnetism, et al) then it would only be subject to eddy currents as it moved through magnetic fields, and the eddy currents would slow it. – Hot Licks Jan 31 '15 at 20:15

Emf on a conducting object induces eddy currents. These in turn decay due to the electrical resistance of the object. What you end up with is energy in the form of heat.

When you compare the two objects (essentially a conductor versus a non-conductor), a portion of the potential gravitational energy goes into generating eddy currents. That means the conductor has less kinetic energy and hence a slower speed.

Whether this is actually measurable (even in vacuum) is doubtful at best. I have a question for you also:

You seem to mixing up magnetic force and emf - in your example, what generates the emf?

• Sorry but how can you say that "a portion of the potential gravitational energy goes into generating eddy currents" ? – jonsno Mar 15 '17 at 15:15

Read the blue box in NCERT on page no 219 with the heading "ELECTROMAGNETIC DAMPING". If we do the experiment in a aluminium pipe, then due to eddy curretns the glass bob will reach first as the motion of spherical bob is opposed.

BUT if we do the experiment in a PVC/Plastic pipe or in air...both will reach at same time.

Since both the balls will be at gravitational equipotential surface, they will fall with same velocity. While the distance for both the balls is same (i.e. they have the same height), time will also be same for both.

Same time! If they have same densities, and same surface area exposed to air resistance.

• It only states that they are the same size. They could have different mass since glass has a lower density than most metals. Although they might have the same average densities if the metallic sphere has a hollow space. – LDC3 Jan 31 '15 at 4:58

The glass bob will reach the ground earlier as acceleration due to gravity is independent of a falling body's mass. Being an insulator, no induced current is developed in it due to Earth's magnetic field.

Both Air resistance and height play an important role which determines the time of flight for two objects of different masses dropped from same height. Objects fall at the same rate(constant acceleration) if the effect of air resistance is negligible. If two objects of different masses are dropped from very large height(eg from an air craft) then the objects with greater mass fall faster than the lighter one. This is due to the faster balancing of forces (weight and air resistance) for the lighter object than the heavier object. If the height from which objects dropped is small, then the variation in time of flight will be too small to measure accurately. The above answer is valid assuming no electromagnetic effect on falling objects due to eddy currents.

The glass sphere will reach the ground earlier, because as the metallic sphere is freely falling within the magnetic field of the earth, a large amount of current will be induced on the metallic sphere called eddy current. The eddy current will oppose its cause and the cause is the acceleration of the metallic sphere. Now it will stop the metallic sphere to fall so the speed of the metallic sphere will decrease and hence the glass sphere will reach the ground earlier.

In metallic ball there will be electromagnetic induction , according to lenz law emf will be induced and it will oppose the flow of its motion , so metallic ball will reach a bit late than glass ball...

The glass bob reaches faster. when the two bobs are freely falling the metallic ball which is conducting, produces a current on its surface called eddy currents which opposes the direction of the acceleration i.e. opposite to gravitational acceleration. and hence reduces the speed of the metallic ball which falls under the earth's magnetic field this effect is also called electromagnetic damping. but since glass ball which is insulating doesn't produce any kind of eddy current on its surface therefore glass bob reaches faster without any hindrances.

i think that both the bobs will reach the ground at same time because mass of both are nearly the same as they are of equal sizes and consideration of earth's magnetic field is not very effective in my point of view.

Glass bob reaches first because there is no effect of electro magnetic induction in it due to presence of earths magnetic field Unlike metal bob (Answer from cbse exam paper _2014 )

• As it stands, this answer doesn't contain enough information to be a good answer. Flesh it out a bit, add some details. – Pranav Hosangadi Jan 13 '15 at 15:24

Think about the density of Lithium which is lower than the density of glass. The lithium ball many hit the ground later than the more dense glass due to air resistance. The experiment requires a procedure to put coating on the lithium ball to avoid it from burning in air.

The glass ball reached the ground earlier because no current is generated due to earth gravitational force.

• As the questioner points out "Magnetic force will be perpendicular to velocity hence no work done by it." so your answer will need to address that point. – Brandon Enright Dec 4 '14 at 6:25

If we throw the same size of metal box and a glass box. The glass box will reach first coz in the metallic sphere as it is coming closer to the earth's magnetic field with velocity v,it will produce eddy currents in it and to this result it will repel the earth gravitational force by lenz law, so in metallic box the gravitational force acting will be less than the real gravitational force. This is not so the case in glass box as magnetic field will have no effect on it. Thus it will be coming down with same real gravitational force and thus,will reach first as compared to metallic sphere of same size.

Hope u understood

metal ball would hit the ground first. there wouldn't be any effect of induce emf or magnetic field. it only depends on gravitational force, as F=mg the mass of metal ball is greater, therefore, it will reach faster than glass ball, whose mass is less than metal ball.

• Galileo dislikes you. – Nick Mar 5 '15 at 11:03