SATHEE: Centre of Mass 3 Question 13

Centre of Mass 3 Question 13

16. A ball of mass $0.2 k g$ rests on a $v m / s$ vertical post of height $5 m$ . A bullet of mass $0.01 k g$ , travelling with a velocity $v m / s$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet

travel independently. The ball hits the ground at a distance of $20 m$ and the bullet at a distance of $100 m$ from the foot of the post. The initial velocity $v$ of the bullet is

(2011)

(a) $250 m / s$

(b) $250 \sqrt{2} m / s$

(d) $500 m / s$

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Answer:

Correct Answer: 16. (d)

Solution:

$\begin{aligned} R & = u \sqrt{\frac{2 h}{g}} \Rightarrow 20 = v_{1} \sqrt{\frac{2 \times 5}{10}} \\ and & 100 = v_{2} \sqrt{\frac{2 \times 5}{10}} \\ \Rightarrow v_{1} & = 20 m / s, v_{2} = 100 m / s . \end{aligned}$

Applying momentum conservation just before and just after the collision

$(0.01) (v) = (0.2) (20) + (0.01) (100) v = 500 m / s$

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Centre of Mass 3 Question 13

16. A ball of mass 0.2kg rests on a vm/s vertical post of height 5m. A bullet of mass 0.01kg, travelling with a velocity vm/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet

Answer:

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16. A ball of mass $0.2 k g$ rests on a $v m / s$ vertical post of height $5 m$ . A bullet of mass $0.01 k g$ , travelling with a velocity $v m / s$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet