At the given time, y = m₁ ⇒ x₀
After 't' time, y = m₂x + c ⇒ 0.1 m
The mass m₁ is given as:
m₁ = 10⁻³/0.1 = 10⁻² kg
The mass m₂ is given as:
m₂ = 10⁻³/0.05 = 2 × 10⁻² kg
The kinetic energy is given as:
dK = 1/2 dmV²
dK = 1/2 μ.dx (-V. ∂y/∂x)²
∫dK = 1/2 μ.V² [m₁² dx + m₂² dx]
Now, the velocity is given as:
V = √(T/μ)
Now, the kinetic energy becomes,
K = 1/2 T [m₁² (0.1) + m₂² (0.5)]
On substituting the values, we get,
K = 1/2 (10) [(10⁻⁴)² (0.1) + (4 × 10⁻⁴)² (0.5)]
K = 10/2 [10⁻⁴](0.3)
∴ K = 0.15 mJ
