A metre stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency f0. If the bottom half of the stick were cut off, then its new frequency of small oscillation would become

Question

A metre stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency f0. If the bottom half of the stick were cut off, then its new frequency of small oscillation would become (A) f0 (B) √2 f0 (C) 2 f0 (D) 2 √2 f0

Tardigrade Admin · Accepted Answer

f0=(1/2 π) √(m g l/I) where l is the distance between point of suspension and centre of mass of the body. Thus, for the stick of length L and mass m, f0 prime=(1/2 π) √(m g (L/4)/(m)2 ((L / 2)2)12 =(1/2 π) √(12 g/L)=√2 f0

Q. A metre stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency $f_{0}$ . If the bottom half of the stick were cut off, then its new frequency of small oscillation would become

$f_{0}$

$2 f_{0}$

$2 f_{0}$

$22 f_{0}$

Q. A metre stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency f0​. If the bottom half of the stick were cut off, then its new frequency of small oscillation would become

f0​

2​f0​

2f0​

22​f0​

f0​=2π1​Imgl​​ where l is the distance between point of suspension and centre of mass of the body. Thus, for the stick of length L and mass m, f0′​=2π1​2m​12(L/2)2​mg4L​​​ =2π1​L12g​​=2​f0​

Q. A metre stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency $f_{0}$ . If the bottom half of the stick were cut off, then its new frequency of small oscillation would become

$f_{0}$

$2 f_{0}$

$2 f_{0}$

$22 f_{0}$