Question

A spring of spring constant $200N{m}^{-1}$ has a block of mass $1kg$ hanging at its one end and from another end, spring is attached to a ceiling of an elevator. The elevator rising upwards with an acceleration of $g/3$ . When acceleration suddenly ceases, then angular velocity and elongation during the time when the elevator is accelerating

• A. $14.14rad{s}^{-1},0.07m$
• B. $13rad{s}^{-1},0.1m$
• C. $14rad{s}^{-1},0.05m$
• D. $10rad{s}^{-1},0.07m$

Answer 1

Answer: (A)

The angular frequency under all circumstances is
$\omega =\sqrt{\left(\frac{\text{k}}{\text{m}}\right)}$
$=\sqrt{\left(\frac{200}{1}\right)}=14\text{.}14\text{ rad}/\text{s}$

When elevator is moving up, using NLM
$\text{T}-\text{mg}=\frac{\text{mg}}{3}\Rightarrow \text{T}=\frac{4\text{mg}}{3}$
This tension elongates the spring by x
$\text{T}=\text{kx}\Rightarrow \text{x}=\frac{4\text{mg}}{3\text{k}}=0\text{.}07\text{ m}$