## Question

Download Solution PDF# A shell of mass 3 kg explodes in to two fragments of 1 kg and 2 kg. The ratio of momenta of the fragments and the ratio of the kinetic energy of the fragments (lighter ∶ heavier) are respectively:

## Answer (Detailed Solution Below)

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## Detailed Solution

Download Solution PDF**Concept:**

The momentum of a body is the product of the mass of the body and the velocity of the body.

- P = mv
- It is a vector quantity, so it possesses both magnitude and direction.

Principle of conservation of linear momentum

- Linear momentum of a system remains constant (in magnitude and direction) if the external forces acting on the system add up to zero.
- m
_{1}v_{1}+ m_{2}v_{2}= 0 -- (1)

Kinetic energy is defined as the energy that is produced by an object due to its motion.

- The kinetic energy of a moving body, \(K.E.= \frac12mv^2\)
- Where, m = mass of the body, v = velocity of the body

**Calculation:**

When the shell explodes in to two fragments then from the principle of conservation of linear momentum, the momenta of the fragments are equal, and the direction of momenta is opposite.

**The ratio of momenta of the fragments is 1:1**

Let the m1 = 1 kg and m2 = 2 kg

m_{1}v_{1} = -m_{2}v_{2}

⇒ 1 × v_{1} = - 2 × v_{2}

⇒** ****v _{1} = -2v_{2} **

Now kinetic energy of 1 kg fragments

\(K.E._1= \frac12mv_1^2 = \frac12\times 1\times (2v_2)^2 = 2v_2^2\)

Also, kinetic energy of 2 kg fragments

\(K.E._2= \frac12mv_2^2 = \frac12\times 2\times (v_2)^2 = v_2^2\)

The ratio of the kinetic energy of the fragments (lighter ∶ heavier) is,

**K.E. _{1} : K.E._{2} = 2:1**

Last updated on Feb 14, 2024

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