The energy E of an oscillating body in simple harmonic motion depends on its mass m, frequency n and amplitude A as E=k(m)x(n)y(A)z. The value of (x+y+z) is .

Question

The energy E of an oscillating body in simple harmonic motion depends on its mass m, frequency n and amplitude A as E=k(m)x(n)y(A)z. The value of (x+y+z) is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

By using dimensional analysis M L2 T-2=Mx(T-1)y(L)z=Mx Lz T-y ⇒ x=1, z=2, y=2 ⇒ x+y+z =1+2+2=5

Q. The energy $E$ of an oscillating body in simple harmonic motion depends on its mass $m$ , frequency $n$ and amplitude $A$ as $E = k (m)^{x} (n)^{y} (A)^{z}$ . The value of $(x + y + z)$ is ____.

By using dimensional analysis
$M L^{2} T^{- 2} = M^{x} (T^{- 1})^{y} (L)^{z} = M^{x} L^{z} T^{- y}$
$\Rightarrow x = 1, z = 2,$
$y = 2$
$\Rightarrow x + y + z$
$= 1 + 2 + 2 = 5$

Q. The energy E of an oscillating body in simple harmonic motion depends on its mass m, frequency n and amplitude A as E=k(m)x(n)y(A)z. The value of (x+y+z) is ____.

By using dimensional analysis ML2T−2=Mx(T−1)y(L)z=MxLzT−y ⇒x=1,z=2, y=2 ⇒x+y+z =1+2+2=5

Q. The energy $E$ of an oscillating body in simple harmonic motion depends on its mass $m$ , frequency $n$ and amplitude $A$ as $E = k (m)^{x} (n)^{y} (A)^{z}$ . The value of $(x + y + z)$ is ____.

By using dimensional analysis
$M L^{2} T^{- 2} = M^{x} (T^{- 1})^{y} (L)^{z} = M^{x} L^{z} T^{- y}$
$\Rightarrow x = 1, z = 2,$
$y = 2$
$\Rightarrow x + y + z$
$= 1 + 2 + 2 = 5$