Correct Answer - Option 4 : 125%
The correct answer is option 4) i.e. 125%
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:
Let the initial and final linear momentum be p1 and p2.
Let the initial and final kinetic energy be KE1 and KE2.
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
Let p1 = p
For 50% increase in linear momentum, p2 = 1.5 p1 = 1.5p
Then,
KE1 ∝ p2
KE2 ∝ (1.5p)2
Percentage change in kinetic energy \(= \frac{KE_2 -KE_1}{KE_1} \times 100 \)
\(⇒ \frac{(1.5p)^2 -p^2}{p^2} \times 100 \)
\(⇒ \frac{2.25 - 1}{1} \times 100 = 125\%\)
Thus, the change in kinetic energy is 125%.