A canon shell fired breaks into two equal parts at its highest point. If one part reatraces the path to the canon with kinetic energy `E_1` and kinetic energy of the second part is `E_2` , then

Options

A. `E_2= 15E`
B. `E_2=E_1`
C. `E_2 = 4E_1`
D. `E_2=9E_1`

Answer

D

Explanation

Momentum before explosion
`=u cos theta xx 2 m`
Momentum after explosion
`=- mu cos theta + mv_2`
Mometum is conserved, so `2 mu cos theta =- mu cos theta + mv_2`
`rArr v_2 = 3 u cos theta`
Kinetic energy of first part.
`=E_1 = 1/2 mv_(1)^(2) =1 /2 m (- u cos theta)^2`
`rArr E_1 = 1/2 mu^(2) cos^(2) theta`
Now , kinetic energy of second part
`= E_2 = 1/2 mu^2 cos^2 theta=9E_1`
So, `E_2 = 9E_1`