A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation F = F₀[1 - ((t-T)/T)²]
Where F₀ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is:
A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation F = F₀[1 - ((t-T)/T)²]
Where F₀ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is:
Option 1 -
F₀T/3M
Option 2 -
2F₀T/M
Option 3 -
4F₀T/3M
Option 4 -
F₀T/2M
Asked by Shiksha User
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1 Answer
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Correct Option - 3
Detailed Solution:v = ∫a dt = (1/M)∫F dt
v = (F? /M) ∫ [1 - (t-T)²/T²] dt from 0 to 2T
= (F? /M) [t - (t-T)³/3T²]? ²?
= (F? /M) [ (2T - T³/3T²) - (0 - (-T)³/3T²) ]
= (F? /M) [ 2T - T/3 - T/3 ] = (F? /M) [ 4T/3 ] = 4F? T/3M.
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