Question

If momentum of an object increases by 2% then its kinetic energy increase by

Answer 1

Answer:

Let the initial mass of the body be m and its velocity be v. 

Initial momentum of the body = mv 

Initial KE = mv^2/2 

If the momentum increases by 10%, new momentum = mv + 10% of mv 

= mv + 10/100mv 

= mv + mv/10 

=11mv/10 

=m(11v/10) 

New velocity = 11v/10 

Increase in velocity = v/10 

New KE = m(11v/10)^2/2 

= 121/100mv^2/2 

Increase in KE = 21%

It will be 21%

Thank you

mark as brainlist

Answer 2

Kinetic energy will increase by 4% if the momentum is increased by 2%

Given: Momentum increases by 2%

To Find: The increase in kinetic energy

Solution:

Let the initial momentum be p

Let the final momentum be p'

Let the initial kinetic energy be K

Let the final kinetic energy be K'

The momentum of a body is given as

p = mv, where p is the momentum of the body, m is the mass of the body and v is the velocity of the body.

The kinetic energy of a body is given as

K = $\frac{1}{2}$  mv², where K is the kinetic energy of the body, m is the mass of the body and v is the velocity of the body.

K =  $\frac{1}{2}$ (mv) v                                           since p = mv

  =   $\frac{1}{2}$ pv

   =  $\frac{1}{2}$ p ($\frac{p}{m}$)                                            since v = p/m

K = p² / 2m

Momentum is increased by 2%

Increase in momentum = $\frac{2}{100}$ p

Final momentum = Initial momentum + Increase in momentum

p'   = p + $\frac{2}{100}$ p

p'   = 1.02p

Since the body is the same, the mass will also remain the same

K= p² / 2m

K' = (p')²/ 2m

K' = (1.02)² p² / 2m

K' = 1.04 p² / 2m

K' = 1.04 K

Percentage change in kinetic energy = $\frac{Final Kinetic Energy - Initial Kinetic Energy}{Initial Kinetic Energy}$  x100

Percentage change in kinetic energy = $\frac{1.04K - K}{K}$ x 100

                                                              = 4%

Therefore, the kinetic energy will increase by 4% if the momentum is increased by 2%