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Answer:
b)
this is correct 110000009% sure.
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Explanation:
Velocity of the particle executing SHM at any ins_tant is defined as the time rate of change of its displacement at that ins_tant.
Let the displacement of the particle at an ins_tant t is given by
x = a sinωt
∴ Velocity v = dx / dt = d ( a sinωt ) / dt
= aωcos ωt = aω √ ( 1 - sin^2 ωt )
= aω √ [ 1 - ( x^2 / a^2) ] = ω √ ( a^2 - x^2 )
At mean positon, x = 0
∴ vmax = ωa
According to problem,
v = vmax /2 = aω / 2
But v = ω √ a^2 - x^2
∴ aω / 2 = ω √( a^2 - x^2 ) or x = √3 / 2 a
∴ Option b is the correct answer !
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