Question

Three masses 100g, 300g and 500g are suspended at the end of a spring as shown in figure and are in equilibrium. When the 500 g mass is removed, the system oscillates with a period of 3 second. When the 300 g mass is also removed, it will oscillate with a period of

• A. \(1.0\) s
• B. \(1.5\) s
• C. \(2.0\) s
• D. \(2.5\) s

Hint:

T = 2 pi sqrt(m/k), so T is proportional to sqrt(m). Compare 400 g with 100 g.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In the figure, a spring hangs from a support, and three blocks of 100 g, 300 g and 500 g are stacked one below the other at its lower end. The time period of a mass on a spring depends on the mass attached.

Step 2: Key Formula or Approach:
\[ T = 2\pi\sqrt{\frac mk} \Rightarrow T\propto\sqrt m \]

Step 3: Detailed Explanation:
When the 500 g block is removed, the blocks of 100 g and 300 g stay, so the oscillating mass is 400 g and \(T_1 = 3\) s.
When the 300 g block is also removed, only the 100 g block remains.
\[ \frac{T_2}{T_1} = \sqrt{\frac{100}{400}} = \frac12 \]
\[ T_2 = \frac{3}{2} = 1.5 \text{ s} \]
Option (A) 1.0 s would need a mass ratio of 1/9, and (C) 2.0 s would need 4/9. Option (D) 2.5 s would need a mass larger than 100 g.

Final Answer:
The period with only the 100 g block is 1.5 s, option (B). \[ \boxed{1.5 \text{ s (B)}} \]