Question 178 of 194

Two bodies of masses $1kg$ and $4kg$ are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency $25rad{s}^{-1}$, and amplitude $1.6cm$ while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take $g=10m{s}^{-2}$).

A$20N$B$60N$C$40N$D$10N$

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Answer: (B) $60N$

Given $\omega =25rad/s$ and A = 1.6 cm

$∴\omega =\sqrt{\dfrac{\text{k}}{\text{m}}}=25$ $\Rightarrow k={25}^{2}$

Maximum compression in the spring

$={x}_{\text{o}}+A$

$=\dfrac{\text{mg}}{\text{k}}+\text{A}$

$∴$${F}_{max}=4g+k({x}_{0}+A)$
${F}_{max}=4g+k\left(\dfrac{\text{mg}}{\text{k}}+\text{A}\right)$

$=40+20=60N$