Question

If the momentum of a body is increased by n times, then the kinetic energy-
1. decreases by a multiple of n
2. increases by a multiple of n²
3. decreases by a multiple of 0.5n
4. increases by a multiple of 0.5n2

Answer 1

Correct Answer - Option 2 : increases by a multiple of n²

The correct answer is option 2) i.e. increases by a multiple of n2

CONCEPT:

• ​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.
• 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

EXPLANATION:

We know, \( KE =\frac{1}{2} mv^2\)

Multiplying and dividing by m we get,  

\(⇒ KE =\frac{1}{2} mv^2 \times \frac{m}{m} = \frac{p^2}{2m}\)

⇒ KE ∝ p²

So, if the momentum increases by n times, 

⇒ KE ∝ (np)²

⇒ KE ∝ n²p

• Thus, if the momentum of a body is increased by n times, then the kinetic energy increases by a multiple of n2.