An object of mass m is suspended at the end of a massless wire of length L and area of cross- section, A. Young modulus of the material of the wire is Y . If the mass is pulled down slightly its frequency of oscillation along the vertical direction is:

Question

An object of mass m is suspended at the end of a massless wire of length L and area of cross- section, A. Young modulus of the material of the wire is Y . If the mass is pulled down slightly its frequency of oscillation along the vertical direction is: (A) f =(1/2 π) √( YA / mL ) (B) f =(1/2 π) √( YL / mA ) (C) f =(1/2 π) √( mA / YL ) (D) f =(1/2 π) √( mL / YA )

Tardigrade Admin · Accepted Answer

An elastic wire can be treated as a spring with k =( YA /ℓ) T =2 π √( m / k ) f =(1/2 π) √( k / m )=(1/2 π) √( YA / m ℓ)

Q. An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross- section, $A$ . Young modulus of the material of the wire is $Y .$ If the mass is pulled down slightly its frequency of oscillation along the vertical direction is:

$f = \frac{1}{2 π} \frac{Y A}{m L}$

$f = \frac{1}{2 π} \frac{Y L}{m A}$

$f = \frac{1}{2 π} \frac{m A}{Y L}$

$f = \frac{1}{2 π} \frac{m L}{Y A}$

An elastic wire can be treated as a spring with
$k = \frac{Y A}{ℓ}$
$T = 2 π \frac{m}{k}$
$f = \frac{1}{2 π} \frac{k}{m} = \frac{1}{2 π} \frac{Y A}{m ℓ}$

Q. An object of mass m is suspended at the end of a massless wire of length L and area of cross- section, A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is:

f=2π1​mLYA​​

f=2π1​mAYL​​

f=2π1​YLmA​​

f=2π1​YAmL​​