Two bodies of masses 1kg and 4kg are connected to a vertical...

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}

Two bodies of masses 1kg and 4kg are connected to a vertical spring, as shown in the figure. The smaller mass executes

Options

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

Correct answer

B. $60N$

Step-by-step solution

Two bodies of masses 1kg and 4kg are connected to a vertical spring, as shown in the figure. The smaller mass executes
Given $\omega = 2 5 rad/s$ and A = 1.6 cm

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

Maximum compression in the spring

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

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

$∴$ ${F}_\max = 4g + k ( {x}_{0} + A )$

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

$= 40 + 20 = 60N$

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