# If the linear momentum of a body is increased by 50%, the increase in kinetic energy will be-

20 views
in Physics
closed
If the linear momentum of a body is increased by 50%, the increase in kinetic energy will be-
1. 50%
2. 75%
3. 100%
4. 125%

by (30.0k points)
selected

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%.