Question

if the linear momentum of an object is increased by 0.1 % then the kinetic energy is increased by​

Answer 1

Answer:

See the attachment

Explanation:

Answer 2

Relationship between kinetic energy and Linear momentum

Relationship between kinetic energy and Linear momentum

$\frac{ {p}^{2} }{2m} = K \:$

Mass of the object can't change.

So, We can say

$\boxed{ \frac{p _{1} ^{2} }{ p_{2} ^{2} } = \frac{K_{1}}{K_{2}} } \\ \\ \boxed{ \frac{p _{1} }{ p_{2} } = \sqrt{\frac{K_{1}}{K_{2}} }} \\ \\ \boxed{ \frac{p _{2} }{ p_{1} } = \sqrt{\frac{K_{2}}{K_{1}} }}$

Now,

Given Linear momentum is increased by 0.1 %

Let p be the initial linear momentum

K1 be the initial kinetic energy

Let the new kinetic energy be K2

New linear momentum = 1.001 p

New kinetic energy will be,

⇒ 1.001 p / p = √ ( K2 / K1)

⇒ (1.001)² = K2 / K1

⇒K2 = 1.002001 K1

Now,

K2 - K1 = 1.002001 K1 - K1 = 0.002001 K1

Now % change in Kinetic energy,

⇒ 0.002001 K1/K1 * 100

⇒ 0.002001 * 100

⇒ 0.2001 %

Therefore, The percentage change in Kinetic energy will approximately be 0.2 %