A bullet of mass m_1 is fired horizontally with a speed v_0 into the bob of a ba

Question

A bullet of mass m_1 is fired horizontally with a speed v_0 into the bob of a ballistic pendulum of mass m_2. The bob is attached by a massless string. The bullet is stopped in the bob. Apply conservation of linear momentum and mechanical energy to calculate the maximum height h reached by the bob and bullet assembly. The correct expression for h as a function of m_1, m_2, v_0, and g is: (a) h = m_1/m_1 + m_2. v_0^2/2g (b) h = m_1^2/(m_1 + m_2). v_0^2/2g (c) h = m_1/m_2. v_0^2/2g (d) h = m_1 m_2/(m_1 + m_2)^2. v_0^2/2g

Explanation / Answer

Option (a) is the correct answer.

Explanation:

Initial kinetic energy of the bullet, E1 = 0.5*m1*v0^2

Potential energy gained by the system, E2 = (m1+m2)*g*h

Equating these two -

0.5*m1*v0^2 = (m1+m2)*g*h

=> h = m1*v0^2/2*(m1+m2)*g

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