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The speed $υ$ of a particle moving along a straight line, when it is at a distance (x) from a fixed point of the line, is given by $υ^{2} = 108 - 9 x^{2}$ (all quantities are in CGS units):

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the motion is uniformly accelerated along the straight line

the magnitude of the acceleration at a distance 3cm from the fixed point is

27 {cm/sec}^{2}

the motion is simple harmonic about the given fixed point

the maximum displacement from the fixed point is 4 cm

answer is C.

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Detailed Solution

Compare given equation with stranded equation

V = ω \sqrt{A^{2} - x^{2}}

$v = 3 \sqrt{{(\sqrt{12})}^{2} - x^{2}}$

$ω = 3, A = \sqrt{12}$

$a = ω^{2} x = 9 \times 3 = 27 c m / s^{2}$

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