1. Tardigrade
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  3. Physics
  4. The time period of oscillation of a body is given by T=2π√(mgA/K) K represents the kinetic energy, m mass, g acceleration due to gravity and A is unknown. If [A] = MxLyTZ ; then what is the value of x + y + z ?

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Q. The time period of oscillation of a body is given by $T=2\pi\sqrt{\frac{mgA}{K}}$
$K$ represents the kinetic energy, $m$ mass, $g$ acceleration due to gravity and $A$ is unknown.
If $[A] = M^xL^yT^Z$ ; then what is the value of $x + y + z$ ?

Physical World, Units and Measurements

Solution:

$\left[T\right]=\left[\left(\frac{mgA}{K}\right)^{1/2}\right]=\left[\frac{mgA}{\left(mv^{2}\right)}\right]^{1/2}=\left[\frac{A}{vT}\right]^{1/2}=\left[\frac{A}{L}\right]^{1/2}$
$\Rightarrow \left[A\right]=\left[M^{0}LT^{2}\right]$
$\Rightarrow \left[M^{x}L^{y}T^{z}\right]=\left[M^{0}LT^{2}\right]$
$\Rightarrow x=0$, $y=1$, $z=2$
$\Rightarrow x+y+z=3$