SATHEE: Work Energy and Power - Result Question 50

Work Energy and Power - Result Question 50

53. A body of mass $(4 m)$ is lying in $x - y$ plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is :

[2014]

(a) $m v^{2}$

(b) $\frac{3}{2} m v^{2}$

(d) $4 m v^{2}$

Show Answer

Answer:

Correct Answer: 53. (b)

Solution:

(b) By conservation of linear momentum Magnitude of the momentum of heavier piece of mass $(2 m) =$ Magnitude of the vector sum of momentum of each piece of mass (m)

$\begin{aligned} (2 m) v_{1} = \sqrt{(m v)^{2} + (m v)^{2}} \\ \Rightarrow & 2 m v_{1} = \sqrt{2} m v \Rightarrow v_{1} = \frac{v}{\sqrt{2}} \end{aligned}$

As two masses of each of mass $m$ move perpendicular to each other.

Total KE generated

$= \frac{1}{2} m v^{2} + \frac{1}{2} m v^{2} + \frac{1}{2} (2 m) v_{1}^{2}$

Play Store

App Store

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Work Energy and Power - Result Question 50

53. A body of mass (4m) is lying in x−y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is :

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

53. A body of mass $(4 m)$ is lying in $x - y$ plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is :