Question

A bullet of mass 25 gram moving at a speed of 240 m/sec embeded in a block of mass 2 kg suspended by a string. To what height the block and bullet system get raised.​

Answer 1

Given:

• Mass of bullet = m = 25 gram
• Speed of bullet = v= 240m / sec
• Mass of block = M = 2kg = 2000 g

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Need to find:

• Height the block and bullet get raised = h =?

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Solution:

By applying conversation of mechanical energy ( which states that energy can neither be created nor destroyed, but can only be transformed from one form to another), we get:

Initial Kinetic Energy= Final Potential Energy

→ The KE of the system during collision = PE of the system at the time of observation

→ $\dfrac{1}{2} (m + M) {v}^{2} = (m + M)gh$

Substitute the values!

→$\dfrac{1}{2} (25 \times 2000) \times {240}^{2} = (25 + 2000) \times 10 \times h$

→$\dfrac{2025 \times 240 \times 240}{2} = 2025 \times 10 \times h$

→$h = \dfrac{2025 \times 240 \times 240}{2 \times 2025 \times 10}$

→$h = 240 \times 12m$

→$\red{\bold{\boxed {\large{h = 2880 \: m}}}}$

∴ The system will rise to a height of 2880m