SATHEE: Centre of Mass 3 Question 34

Centre of Mass 3 Question 34

37. A body of mass $1 k g$ initially at rest, explodes and breaks into three fragments of masses in the ratio $1 : 1 : 3$ . The two pieces of equal mass fly-off perpendicular to each other with a speed of $30 m / s$ each. What is the velocity of the heavier fragment?

(1981, 3M)

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Answer:

Correct Answer: 37. $10 \sqrt{2} m / s$ at $45^{\circ}$

Solution:

From conservation of linear momentum $p_{3}$ should be equal and opposite to $p_{12}$ (resultant of $p_{1}$ and $p_{2}$ ). So, let $v^{'}$ be the velocity of third fragment, then

$(3 m) v^{'} = \sqrt{2} m v \Rightarrow ∴ v^{'} = \frac{\sqrt{2}}{3} v$

Here, $v = 30 m / s$ (given) $\Rightarrow v^{'} = \frac{\sqrt{2}}{3} \times 30 = 10 \sqrt{2} m / s$

This velocity is at $45^{\circ}$ as shown in figure.

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Centre of Mass 3 Question 34

37. A body of mass 1kg initially at rest, explodes and breaks into three fragments of masses in the ratio 1:1:3. The two pieces of equal mass fly-off perpendicular to each other with a speed of 30m/s each. What is the velocity of the heavier fragment?

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37. A body of mass $1 k g$ initially at rest, explodes and breaks into three fragments of masses in the ratio $1 : 1 : 3$ . The two pieces of equal mass fly-off perpendicular to each other with a speed of $30 m / s$ each. What is the velocity of the heavier fragment?