Question

An object of mass \(10 \, \text{kg}\) is released from rest in a liquid. If the object moves a distance of \(2 \, \text{m}\) while sinking in a time duration of \(1 \, \text{s}\), then the mass of the liquid displaced by the submerged object is (Given: Acceleration due to gravity \( g = 10 \, \text{m/s}^2 \))

• A. \( 5 \, \text{kg} \)
• B. \( 6 \, \text{kg} \)
• C. \( 3 \, \text{kg} \)
• D. \( 4 \, \text{kg} \)

Hint:

Use \( s = \frac{1}{2} a t^2 \) to find acceleration, and apply Newton’s law \( W - B = ma \) to relate buoyancy with displaced mass.

Answer 1

The Correct Option is B

Given: - \( m = 10 \, \text{kg} \)
- \( s = 2 \, \text{m} \)
- \( t = 1 \, \text{s} \)
- \( g = 10 \, \text{m/s}^2 \)
Using the equation of motion: \[ s = \frac{1}{2} a t^2 \Rightarrow 2 = \frac{1}{2} a (1)^2 \Rightarrow a = 4 \, \text{m/s}^2 \] Let \( F_{\text{net}} = ma = 10 \times 4 = 40 \, \text{N} \) The object experiences: - Downward force (weight): \( W = mg = 10 \times 10 = 100 \, \text{N} \)
- Upward force (buoyancy): \( B \)
Using Newton’s second law: \[ W - B = F_{\text{net}} \Rightarrow 100 - B = 40 \Rightarrow B = 60 \, \text{N} \] Buoyant force equals the weight of liquid displaced: \[ B = m_{\text{liquid}} \cdot g \Rightarrow 60 = m_{\text{liquid}} \cdot 10 \Rightarrow m_{\text{liquid}} = 6 \, \text{kg} \]