Q. A block of mass $1\, kg$ is pressed against a spring of force constant $400\, N / m$. The spring is compressed by $10\, cm$ and block is released. Which of the following is a possible velocity of the block during subsequent motion?

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A

2 m / s

B

1 m / s

C

3 m / s

D

4 m / s

Solution:

$\frac{1}{2} m v_{\max }^{2}=\frac{1}{2} k x^{2}$
$v_{\max }=\sqrt{\frac{k}{m}} x=\sqrt{\frac{400}{1}} \times 1=2\, m s ^{-1}$
As the maximum speed is $2\, m / s$, hence the range of speed should be between $0$ and $2\, m / s$.
Hence, options (1) and (2) are correct.

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Q. A block of mass $1\, kg$ is pressed against a spring of force constant $400\, N / m$. The spring is compressed by $10\, cm$ and block is released. Which of the following is a possible velocity of the block during subsequent motion?

2 m / s

1 m / s

3 m / s

4 m / s

$\frac{1}{2} m v_{\max }^{2}=\frac{1}{2} k x^{2}$ $v_{\max }=\sqrt{\frac{k}{m}} x=\sqrt{\frac{400}{1}} \times 1=2\, m s ^{-1}$ As the maximum speed is $2\, m / s$, hence the range of speed should be between $0$ and $2\, m / s$. Hence, options (1) and (2) are correct.

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$\frac{1}{2} m v_{\max }^{2}=\frac{1}{2} k x^{2}$
$v_{\max }=\sqrt{\frac{k}{m}} x=\sqrt{\frac{400}{1}} \times 1=2\, m s ^{-1}$
As the maximum speed is $2\, m / s$, hence the range of speed should be between $0$ and $2\, m / s$.
Hence, options (1) and (2) are correct.