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In a spring block system, match the following. (Only variables mentioned in Column-I are changed, other variables are kept constant.)
COLUMN-I
COLUMN-II
A)
If the mass of the block is doubled.
P)
Energy of oscillation becomes 4 times.
B)
If amplitude of oscillation is doubled.
Q)
Speed of particle becomes 2 times.
C)
If force constant is doubled.
R)
Time period becomes $\sqrt{2}$ times.
D)
If angular frequency is doubled.
S)
Potential energy becomes 2 times.

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$A - R, B - P, C - R, D - S$

$A - S, B - P, C - S, D - R$

$A - S, B - Q, C - S, D - R$

$A - R, B - P, C - S, D - Q$

answer is D.

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Detailed Solution

$T = 2 π \sqrt{\frac{m}{k}}$ if man is doubled
$T_{f} = \sqrt{2} T$
$E = \frac{1}{2} m ω^{2} A^{2} ∴$ Energy becomes 4 times
$E = \frac{1}{2} K A^{2} ∴$ If K is doubles energy doubles
$V = A ω ∴$ $ω$ is doubled then velocity is also doubled

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