Question

In the arrangements shown in figure,masses of each ball are 1 kg and mass of trolley is 4 kg. In the figure shell of mass 1 kg moving horizontally with velocity v = 6 m/sec collides with the ball and get stuck to it .It's maximum deflection of the thread (length 1.5 m) with vertical is:

• A. ${53}^{\circ }$
• B. ${37}^{\circ }$
• C. ${30}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B

${37}^{\circ }$

Conserving the momentum of two balls before and after collision in horizontal direction

$1\times 6=(1+1)\times v$

$v=3m/sec$

Now at the instant of maximum deflection ball will be moving horizontal with same speed as of trolley (i.e., velocity of ball w.r.t. trolley will be 0).

Let it be $v_0$

$2\times 3=(4+2)\times v_0$

Now conserving energy

$\{\frac{1}{2}\times 2\times 3^2\}-\{2\times 10\times 1.5(1-cos\theta \left)\right\}=\{\frac{1}{2}\times 2\times v^2\}+\{\frac{1}{2}\times 4\times v^2\}$