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BITSAT 2021 Paper

Section: Physics

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Question : 9 of 150

Marks: +1, -0

Four massless springs whose force constants are

2k, 2k, k

2k

respectively are attached to a mass

M

kept on a frictionless plane (as shown in figure). If the mass

M

is displaced in the horizontal direction, then the frequency of the system

$\frac{1}{2\pi}\sqrt{\frac{4k}{M}}$
$\frac{1}{\pi}\sqrt{\frac{k}{M}}$
$\frac{1}{2\pi}\sqrt{\frac{k}{7M}}$
$\frac{1}{2\pi}\sqrt{\frac{7k}{M}}$

Solution:

Two springs on the L.H.S. of mass

M

are in series and two springs on the R.H.S. of mass M are in parallel. These combinations of springs will be considered in parallel to mass

M

. Thus effective spring constant,

K=\frac{2k \times 2k}{2k+2k}+(k+2k)=4k

\therefore \text{Frequency}\ v=\frac{1}{2\pi}\sqrt{\frac{K}{M}}=\frac{1}{2\pi}\sqrt{\frac{4k}{M}}.

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