The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

Question

The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be (A) T/4 (B) T (C) T/2 (D) 2T

Tardigrade Admin · Accepted Answer

T =2 π √( m / k ) When the spring is cut into four equal parts, the spring constant of one part will becomes 4 k, therefore the new time period will become T prime=2 π √( m / k prime) T =2 π √( m /4 k ) T prime=( T /2)

Q. The time period of mass suspended from a spring is $T$ . If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

T/4

T

T/2

2T

$T = 2 π \frac{m}{k}$
When the spring is cut into four equal parts, the spring constant of one part will becomes $4 k$ , therefore the new time period will become
$T^{'} = 2 π \frac{m}{k ^{'}}$
$T = 2 π \frac{m}{4 k}$
$T^{'} = \frac{T}{2}$

Q. The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

T/4

T

T/2

2T

T=2πkm​​ When the spring is cut into four equal parts, the spring constant of one part will becomes 4k, therefore the new time period will become T′=2πk′m​​ T=2π4km​​ T′=2T​

Q. The time period of mass suspended from a spring is $T$ . If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

$T = 2 π \frac{m}{k}$
When the spring is cut into four equal parts, the spring constant of one part will becomes $4 k$ , therefore the new time period will become
$T^{'} = 2 π \frac{m}{k ^{'}}$
$T = 2 π \frac{m}{4 k}$
$T^{'} = \frac{T}{2}$