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Standard XII

Physics

Pressure vs Velocity

A weightless ...

Question

A weightless spring of length $60 c m$ and force constant $200 N / m$ is kept straight and unstretched on a smooth horizontal table and its ends are rigidly fixed. A mass of $0.25 k g$ is attached at the middle of the spring and is slightly displaced along the length. The time of the oscillation of the mass is

\frac{π}{20} s

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\frac{π}{10} s

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\frac{π}{5} s

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\frac{π}{\sqrt{200}} s

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Solution

The correct option is C $\frac{π}{20} s$
System is equivalent to parallel combination of springs
$∴ K_{e q} = K_{1} + K_{2} = 400$

and the time period of oscillation is given by:
$T = 2 π \sqrt{\frac{m}{K_{e q}}}$

$= 2 π \sqrt{\frac{0.25}{400}} = \frac{π}{20}$

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The correct option is C π20 sSystem is equivalent to parallel combination of springs ∴Keq=K1+K2=400 and the time period of oscillation is given by:T=2π√mKeq=2π√0.25400=π20

The correct option is C $\frac{π}{20} s$
System is equivalent to parallel combination of springs
$∴ K_{e q} = K_{1} + K_{2} = 400$

and the time period of oscillation is given by:
$T = 2 π \sqrt{\frac{m}{K_{e q}}}$

$= 2 π \sqrt{\frac{0.25}{400}} = \frac{π}{20}$