Two objects of mass 5kg and 10kg are allowed to fall from a height of 10m at the same time. Which of these objects will reach the ground first? Which of these objects will have more final velocity? Give reason.
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Explanation:
Solution:
Let position of centre of mass be (xc.m,0)
image
xcm=m1x1+m2x2m1+m2
=5×0+100×105+10
=2002
=66.66cm
xcm=67cm
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Answered by
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Both Objects reaches ground at the same time.
Both Objects will have Same velocity
Given:
- Two objects of mass 5kg and 10kg
- Fall from a height of 10m
To Find:
- Which of these objects will reach the ground first?
- Which of these objects will have more final velocity
Solution:
- TE = KE + PE
- TE = Total Energy
- KE = Kinetic Energy
- PE = Potential Energy
- PE = mgh
- KE = (1/2)mv²
PE at h = 10 m for 5 kg
= 5g10
= 50g
KE = 0 as drop/fall
TE = 50g
Before Striking Grounf
PE = 0 as h =0
KE = (1/2)5v²
TE = (1/2)5v²
Equate Total Energy
(1/2)5v² = 50g
=> v² = 20g
=> v = √20g
Similarly for 10 kg object
(1/2)10v² = 100g
=> v² = 20g
v = √20g
Hence Velocity for Both is same
V = U + at
√20g = 0 + gt
=> t = √(20/g)
Hence Time is also same for both
Both Objects reaches ground at the same time.
Both Objects will have Same velocity
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