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 ?

Question

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 ? (A) 3 (B) 2 (C) 1 (D) 5

Tardigrade Admin · Accepted Answer

[T]=[((mgA/K))1/2]=[(mgA/(mv2))]1/2=[(A/vT)]1/2=[(A/L)]1/2 ⇒ [A]=[M0LT2] ⇒ [MxLyTz]=[M0LT2] ⇒ x=0, y=1, z=2 ⇒ x+y+z=3

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

$3$

$2$

$1$

$5$

$[T] = [(\frac{m g A}{K})^{1/2}] = [\frac{m g A}{( m v ^{2} )}]^{1/2} = [\frac{A}{v T}]^{1/2} = [\frac{A}{L}]^{1/2}$
$\Rightarrow [A] = [M^{0} L T^{2}]$
$\Rightarrow [M^{x} L^{y} T^{z}] = [M^{0} L T^{2}]$
$\Rightarrow x = 0$ , $y = 1$ , $z = 2$
$\Rightarrow x + y + z = 3$

Q. The time period of oscillation of a body is given by T=2πKmgA​​ 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 ?

3

2

1

5

[T]=[(KmgA​)1/2]=[(mv2)mgA​]1/2=[vTA​]1/2=[LA​]1/2 ⇒[A]=[M0LT2] ⇒[MxLyTz]=[M0LT2] ⇒x=0, y=1, z=2 ⇒x+y+z=3

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

$3$

$2$

$1$

$5$

$[T] = [(\frac{m g A}{K})^{1/2}] = [\frac{m g A}{( m v ^{2} )}]^{1/2} = [\frac{A}{v T}]^{1/2} = [\frac{A}{L}]^{1/2}$
$\Rightarrow [A] = [M^{0} L T^{2}]$
$\Rightarrow [M^{x} L^{y} T^{z}] = [M^{0} L T^{2}]$
$\Rightarrow x = 0$ , $y = 1$ , $z = 2$
$\Rightarrow x + y + z = 3$