SIR PLEASE ANSWER MY LITTLE DOUBT.

IF TWO IRON OBJECTS OF THE SAME MASS, ONE BEING A SPHERE AND THE OTHER BEING A CUBOID, ARE DROPPED FROM THE SAME HEIGHT, WHICH OBJECT WILL REACH THE GROUNG FASTER? DOES SURFACE AREA OF THESE OBJECTS PLAY ANY ROLE HERE?

PLEASE PROVIDE A CLEAR AND DETAILED EXPLANATION FOR ME TO UNDERSTAND.

### Asked by kandappan | 30th Sep, 2019, 11:09: AM

### If we neglect air resistance, all the objects dropped from same height will hit the ground at same time.
If we consider air resistance is not negligible, then Object having more surface area will experience more drag force due to air resistance.
Let us consider objects of same mass and same material but different shapes, say, a sphere and cube.
if volume of sphere of radius R is (4/3)πR^{3} , size a of cube that has equal volume is obtained as
(4/3)πR^{3} = a^{3} or a = R (4π/3)^{1/3}
Semi-surface area of sphere which is experiencing drag force is 2πR^{2} ≈ 6.3 R^{2}
Surface area of cube that is subjected to drag force , 5 a^{2} = 5 R^{2} (4π/3)^{2/3} ≈ 13 R^{2}
( when a sphere is moving in air, only half of surface area is facing th air resistance.
Similarly when a cube is moving in air, out of six sids, only 5 sides are facing air resistance )
Hence if we compare the surface area, cube has more surface area.
Hence drag force affecting cube more than sphere. Hence sphere will reach the ground faster

^{3}, size a of cube that has equal volume is obtained as

^{3}= a

^{3}or a = R (4π/3)

^{1/3}

^{2}≈ 6.3 R

^{2}

^{2}= 5 R

^{2}(4π/3)

^{2/3}≈ 13 R

^{2}

### Answered by Thiyagarajan K | 30th Sep, 2019, 05:25: PM

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