Question

Speed v of a particle moving along a straight line,when it is at a distance x from a fixed point on the line is given by $v^2=108-9x^2$ (all quantities in S.I unit).Then

• A. The motion is uniformly accelerated along the straight line
• B. The magnitude of the acceleration along the straight line
• C. The motion is simple harmonic about $x=\sqrt{12}m$
• D. The maximum displacement from the fixed point is 4 cm

Answer 1

The correct option is B The magnitude of the acceleration along the straight line

$v^2=108-9x^2\Rightarrow v=\sqrt{108-9x^2}=\sqrt{9\times 12-9x^2}=3\sqrt{12-x^2}$
comparing it with the velocity in SHM $v=\omega \sqrt{A^2-x^2}$ we have $\omega =3s^{-1}$ and $A=\sqrt{12}m$
the given equation represents a SHM about $x=0$. $\Rightarrow$ C is incorrect.
In SHM
(I) acceleration is not uniform $\Rightarrow$ A is incorrect.
(II) acceleration is along a straight line. $\Rightarrow$ B is correct.
In the given SHM maximum displacement from the mean position is $A=\sqrt{12}m$ $\Rightarrow$ D is incorrect.