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Physics-

General

Easy

Question

An object suspended from a spring exhibits oscillations of period T. Now the spring is cut in two halves and the same object is suspended with two halves as shown in figure. The new time period of oscillation will become

$\frac{T}{2 \sqrt{2}}$
$\frac{T}{2}$
$\frac{T}{\sqrt{2}}$
2T

The correct answer is: $fraction numerator T over denominator 2 end fraction$

Let $k$ be the spring constant of each half part of the spring. For a complete spring, the spring constant $k to the power of ´ end exponent equals k divided by 2$
(springs in series). When two splitted parts of a spring are connected to the body, then the springs are in parallel. Their effective spring constant, $k to the power of ´ end exponent equals k plus k equals 2 k$
As $T equals 2 pi square root of fraction numerator m over denominator k end fraction end root o r blank T proportional to fraction numerator 1 over denominator square root of k end fraction$
$therefore blank fraction numerator T to the power of ´ end exponent over denominator T end fraction equals square root of fraction numerator k divided by 2 over denominator 2 k end fraction end root equals fraction numerator 1 over denominator 2 end fraction o r T to the power of ´ end exponent equals fraction numerator T over denominator 2 end fraction$

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