Question

percentage change in kinetic energy of a body if its momentum is increased by 2%

Answer 1

Answer:

$\bigstar{\bold{Change\:in\:K.E\:=\:4 \%}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Momentum is increased by 2%

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Percentage change in kinetic energy of the body

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ The relation between kinetic energy and momentum is given by the equation

  K. E  = p²/2m ----- equation 1

 where p is the momentum and m is the mass of the body.

→ Given momentum increases by 2%. Let the new momentum be p₁

  p₁ = p + 2/100×p

  p₁ = p + 0.02p

  p₁ = 1.02p

→ Hence kinetic energy will be K.E₁ given by the formula

  K.E₁ = (p₁)²/2m

→ Substituting the value of p₁ we get

 K.E₁ = (1.02p)²/2m

 K.E₁ = 1.04(p²/2m)

→ From the first equation we know this part is given by initial K.E

 K.E₁ = 1.04 × K.E

→ Percentage change in K.E is given by the equatio,

ΔK.E = KE₁ - K.E/K.E × 100

→ Substituting the data, we get

ΔK.E = 1.04 K.E - K.E/K.E × 100

ΔK.E = 0.04 × 100

ΔK.E = 4%

$\boxed{\bold{Change\:in\:K.E\:=\:4\%}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ Kinetic energy is defined as the energy posessed by a body by virtue of its motion.

→ The equations for K.E are

• K.E = 1/2 × m × v²
• K.E = p²/2m

Answer 2

Answer:

exact answer is 3%

Explanation:

you can solve by given formula in the pic