Question:
A bullet moving with speed 200 m/s is just able to pierce a wooden block of 6 cm thickness. What velocity is required to just pierce a block of 8 cm?
A bullet moving with speed 200 m/s is just able to pierce a wooden block of 6 cm thickness. What velocity is required to just pierce a block of 8 cm?
Updated On: Jun 21, 2022
- 400 $ \sqrt{3} $ m/s
- 400 m/s
- 400/ $ \sqrt{3} $ m/s
- 400 $ \sqrt{2} $ m/s
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The Correct Option is A
Solution and Explanation
KE lost by bullet = work done againes plank resistance
$ \frac{1}{2}m{{v}^{2}}=Fx $
Here $ x $ is the distance pierced
$ \frac{v_{2}^{2}}{v_{1}^{2}}=\frac{{{x}_{2}}}{{{x}_{1}}} $
$ \frac{v_{2}^{2}}{40000}=\frac{8}{6} $
$ {{v}_{2}}=\frac{400}{\sqrt{3}}m/s $
$ \frac{1}{2}m{{v}^{2}}=Fx $
Here $ x $ is the distance pierced
$ \frac{v_{2}^{2}}{v_{1}^{2}}=\frac{{{x}_{2}}}{{{x}_{1}}} $
$ \frac{v_{2}^{2}}{40000}=\frac{8}{6} $
$ {{v}_{2}}=\frac{400}{\sqrt{3}}m/s $
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Concepts Used:
Kinetic energy
Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.
