Question

A sphere of mass \(50\) gram is placed on a vertical spring. It is compressed by \(0.4\) m using a force \(10\) N. When the spring is released the sphere will reach to a height of (\(g=10m/s^{2}\))

• A. \(8m\)
• B. \(4m\)
• C. \(2m\)
• D. \(16m\)

Hint:

Find the spring energy from the force and compression, then equate it to the gain in gravitational potential energy.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The elastic energy stored in the compressed spring changes into gravitational potential energy at the highest point.

Step 2: Spring energy
\(k=\dfrac{F}{x}=\dfrac{10}{0.4}=25\) N/m.
\(U=\dfrac{1}{2}kx^2=\dfrac{1}{2}\times25\times0.16=2\) J.

Step 3: Equate to potential energy
\(m=50\) g \(=0.05\) kg.
\(mgh=2\), so \(0.05\times10\times h=2\).

Step 4: Result
\(h=\dfrac{2}{0.5}=4\) m, which is option (B).

Final Answer:
The sphere rises to a height of 4 m. \[ \boxed{\text{(B) }4\,\text{m}} \]