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Two identical metal spheres are released from the top of a tower after t seconds of each other such that they fall along the same vertical line. If the air resistance is neglected then at any instant of time during their fall,

Two identical metal spheres are released from the top of a tower after t seconds of each other such that they fall along the same vertical line. If the air resistance is neglected then at any instant of time during their fall,  

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Grade:11

1 Answers

Vikas TU
14149 Points
5 years ago
Dear Student,
At t = t (when the diference is t between both of them)
For first ball,
x1 = 0 + 0.5gt^2
For second ball which it thrown after time t,
x2 = 0 + 0*0 = 0  
The difference of displacement would be => x1 – x2 = 0.5gt^2
 
Now say after time t’ ,
x1 = 0 + 0.5g(t + t’)^2
and 
x2 = 0 + 0.5gt^2
Differnece would be => x1 – x2 = 0.5g(t + t’)^2 – 0.5gt^2 = 0.5g(t’)(2t + t’)
Which is not the same.
 
 
For speed at time t for first ball and second ball,
v1 = gt
and
v2 = 0
and v1 – v2 = gt
at time after t’
v1 = 0 + g(t + t’)
and 
v2 = 0 + gt’
v1 – v2 = gt + gt’ – gt’ = gt
which is the same.
Hence the speed difference would be constant.
b option.

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