Correct Answer - Option 1 : 1 : 1
The correct answer is option 1) i.e. 1 : 1
CONCEPT:
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Kinetic energy is the energy possessed by a moving object. Kinetic energy (KE) is expressed as:
\(⇒ KE =\frac{1}{2} mv^2\)
Where m is the mass of the object and v is the velocity of the object.
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Momentum: Momentum is the impact due to a moving object of mass m and velocity v.
- The momentum (p) of an object is expressed as:
⇒ p = mv
CALCULATION:
Given that:
Mass of the two bodies:
m1 = 400 g = 0.4 kg
m2 = 200 g = 0.2 kg
The ratio of kinetic energy = \(\frac{KE_1}{KE_2} = \frac{1}{2}\)
We know,
\(⇒ KE =\frac{1}{2} mv^2\)
Multiplying and dividing by m we get,
\(⇒ KE =\frac{1}{2} mv^2 \times \frac{m}{m} = \frac{p^2}{2m}\)
- The relation between momentum and kinetic energy is given by
\(⇒ p =\sqrt{2mKE}\)
- The ratio of linear momentum is given by
\(\Rightarrow \frac{p_1}{p_2} = \frac{\sqrt{2m_1KE_1}}{\sqrt{2m_2KE_2}} =\frac{\sqrt{m_1}}{\sqrt{m_2}} \times\frac{\sqrt{KE_1}}{\sqrt{KE_2}} = \sqrt{\frac{0.4}{0.2}} \times\sqrt{ \frac{1}{2}} = \frac{\sqrt{2}}{1} \times \frac{1}{\sqrt{2}} = \frac{1}{1}\)
