Question

Two objects of masses 2kg and 4kg are moving with the same momentum of 20kg m/s. Will they have same kinetic energy? Will they have same speed?

Answer 1

momentum = mass * velocity

since both have same momentum and different mass

hence velocity will be different and

also kinetic enrgy will be different

v1=20/2

=>10 m/s

v2=20/4

=>5m/s

KE1=1/2mv²

=> 100 joule

KE2=50 joule

Answer 2

The kinetic energy and speed of the two bodies will not be the same.

Step-by-step Explanation:

Given: Mass of the objects $m_1 = 2 \ \text{kg}$ and $m_2 = 4 \ \text{kg}$

Momentum $p_1 = p_2 = 20 \text{kg.m/s}$

To Find: Whether they have the same kinetic energy and speed or not

Solution:

• Whether the objects have the same kinetic energy or not

The kinetic energy of the first object is,

$\Rightarrow KE_1 = \dfrac{1}{2} m_1 v_1^2 = \dfrac{p_1^2}{2m_1} \ \cdots \cdots (1)$

And, the kinetic energy of the second object is,

$\Rightarrow KE_2 = \dfrac{1}{2} m_2 v_2^2 = \dfrac{p_2^2}{2m_2} \ \cdots \cdots (2)$

Dividing (1) and (2), we get

$\Rightarrow KE_1 = 2 KE_2 \Rightarrow KE_1 \neq KE_2$

• Whether the objects have the same speed or not

Since the momentum is equal for both objects, we have,

$\Rightarrow p_1 = p_2$

$\Rightarrow m_1 v_1 = m_2 v_2$

$\Rightarrow 2 \times v_1 = 4 \times v_2$

$\Rightarrow v_1 = 2 v_2 \ \Rightarrow \ v_1 \neq v_2$

Hence, the kinetic energy and speed of the two bodies will not be the same.