Oscillations - Result Question 44
48. A mass of $2.0 kg$ is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is $200 N / m$. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take $g=10 m / s^{2}$ )?
(a) $10.0 cm$
(b) any value less than $12.0 cm$
(c) $4.0 cm$
(d) $8.0 cm$
[2007]
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Answer:
Correct Answer: 48. (a)
Solution:
- (a) Mass gets detached at the upper extreme position when pan returns to its mean position.
At that point, $R=m g-m \omega^{2} a=0$
i.e. $g=\omega^{2} a$
$\Rightarrow a=g / \omega^{2}=m g / k$
$\Rightarrow a=\frac{2 \times 10}{200} \quad[A s=\omega^{2}=\frac{k}{m}]$
$\Rightarrow a=1 / 10 m=10 cm$
