Question

Kinetic energy of a particle is increased by (a) 50% (b) 1% Find percentage change in linear momentum.

Answer 1

Answer:

22.4% approx

Explanation:

P is proportional to root KE

so if KE becomes 1.5 of original then

p becomes 1.224 times the original

means .224 *100 =22.4%

Answer 2

% change in linear momentum will be (a) 22.5% (b) 0.49%

Let initial kinetic energy be K and initial momentum be P of the body

•) Now we know that P=√2mK

Where m is the mass of the body

a) Now kinetic energy is incresed by 50%. Let K' be the new kinetic energy and P' be the new momentum.

•) Now K' = K + 50%K = K + K/2

K' = 3/2K = 1.5K

Now, P' = √2mK'

=> P' = √2m*1.5K = √1.5P

P' = 1.225P

Hence, increase in momentum will be 22.5%

b) Now kinetic energy is incresed by 1%.

•)Now,

K' = K + 1%K = 1.01K

Now , P' = √2mK'

P' = √2m*1.01K = √1.01P

=> P' = 1.0049P

Hence, increse in the momentum will be by 0.49%