Question

When a body of mass $1.0kg$ is suspended from a certain light spring hanging vertically, its length increases by $5cm$. By suspending $2.0kg$ block to the spring and if the block is pulled through $10cm$ and released, the maximum velocity of it in $m/s$ is approximately

(Acceleration due to gravity = $10m/s^2$)

• A. $0.5$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is B $1$

$1\times g=Kx$
$3g=K(x+5)$
$\frac{1}{3}=\frac{x}{x+5}$
$x=2.5$
$10=K\times 2.5\times {10}^2$
$K=400Nhm$
$\omega =\sqrt{\frac{K}{m}}$
$\omega =\sqrt{\frac{400}{3}}$
$V_{max}=A\omega$
$=10\times {15}^2\sqrt{\frac{400}{3}}$
$=1.154m/sec$