Question

A ball of mass $m_b=2\text{kg}$ having initial velocity of $v_b=3\text{m/s}$ hits a ballistic pendulum of mass $m_a=4\text{kg}$ and stick to it. When the ball hits the pendulum it swings up from the equilibrium position and rises up as shown in figure. If length of the pendulum thread is $l=0.1\text{m}$, find maximum deflection of thread with vertical$\left(\theta \right)$.

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. $\text{None of these}$

Answer 1

The correct option is B ${60}^{\circ }$

Before collision

After collision

Applying P.C.L.M
$p_i=p_f$
$m_b{v}_b=(m_a+m_b)v\Rightarrow 2\times 3=(2+4)v\Rightarrow v=1\text{m/s}$
As both ball and pendulum rises up to maximum deflection $\theta$

Using law of conservation of energy,
$\text{Work done by gravity}=\Delta K.E$
$\Rightarrow -(m_a+m_b)gh=(K.E{)}_f-(K.E{)}_i$
$\Rightarrow -(m_a+m_b)gl(1-\cos \theta )=(K.E{)}_f-(K.E{)}_i$
$\Rightarrow -6\times 10\times 0.1(1-\cos \theta )=0-\frac{1}{2}(m_a+m_b)v^2$
$\Rightarrow 1-\cos \theta =0.5\Rightarrow \cos \theta =0.5$
$\therefore \theta ={\cos }^{-1}\left(0.5\right)={60}^{\circ }$