Two small spheres A and B each of mass M hang from ceiling on strings of length ℓ. Sphere A is drawn aside so that it is raised to a height h0 as shown in the figure and then released. Sphere A collides and sticks to sphere B and the combined mass swings to a maximum height equal to

Engineering

Physics

Conservation of Energy

Collision

Momentum and Energy Conservation for System of Particles

Question

Two small spheres A and B each of mass M hang from ceiling on strings of length ℓ. Sphere A is drawn aside so that it is raised to a height h₀ as shown in the figure and then released. Sphere A collides and sticks to sphere B and the combined mass swings to a maximum height equal to

h₀

$\frac{h_{0}}{8}$

$\frac{h_{0}}{2}$

$\frac{h_{0}}{4}$

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Let velocity of A just before collision be $V_{0} = \sqrt{2 {gh}_{0}}$

Velocity of A & B combine is V₀/2 after sticking due to momentum conservation
Maximum height (h) = $\frac{{(V_{0} / 2)}^{2}}{2 g} = \frac{h_{0}}{4}$ .