Question

in a certain system of absolute units the acceleration produced by Gravity in a body falling freely is donated by 5 , the kinetic energy of a 500 kg short moving with the velocity 400 metre per second is denoted by 2000 and its Momentum by 100, then the unit of length, time and mass is​

Answer 1

Answer:

M = 800 kg

L = 3.125 m

T = 1.25 s

Explanation:

in a certain system of absolute units the acceleration produced by Gravity in a body falling freely is donated by 5 , the kinetic energy of a 500 kg short moving with the velocity 400 metre per second is denoted by 2000 and its Momentum by 100, then the unit of length, time and mass is​

acceleration produced by Gravity = 10 m/s²  is denoted by 5

=> 10 m/s²  = 5 L/T²

=> L/T² = 2 m/s²

Kinetic energy = (1/2)mV²  = (1/2)500 * (400)² = 10⁷  kg m²/s²

10⁷  kg m²/s² = 2000 ML²/T²

=> ML²/T² = 5000  kg m²/s²

=> ML (2 m/s²) = 5000  kg m²/s²

=> ML = 2500 kgm

Momentum = mV = 500 * 400 = 200000 kg m/s

200000  kg m/s = 100 ML/T

=> ML/T  = 2000  kg m/s

=> 2500 kgm/T = 2000  kg m/s

=> 1/T = 20/25 /s

=> T = 1.25 s

L/T² = 2 m/s²

=> L /(1.25s)² = 2 m/s²

=> L = 3.125 m

ML = 2500 kgm

=> M (3.125m) = 2500 kgm

=> M = 800 kg

Answer 2

Answer:T=5 sec

L=50m

and M=200kg

Explanation:acceleration(a) produced by gravity(g) in a body falling freely:

We know that v = u+ gt ( here u = 0)

Therefore v=gt =10t m/s

We also know that a=v/t

therefore a= 10t/t m/s^2 = 10 m/s^2

5L/T^2 = 10m/s^2

Therefore L/T^2 = 2 m/s^2 ....................(1)

Now we know that K.E.=1/2 mv^2

2000 ML^2/T^2= 1/2 * 500 * (400)^2 kg m^2/s^2

=> 2000 ML^2/ T^2 = 40000000 kg m^2/s^2...........(2)

Momentum = m*v

100 ML/T = 500*400 kg m/s

=> 100 ML/T = 200000 kg m/s..............(3)

Now by putting the value of L/T^2 in equation (2), we get

2000 ML (2 m/s) = 4* 10^7 kg m^2/s^2

=> ML = 10000 kg m

Now, by putting the value of ML in equation (3), we get

100 * 10000 kg m/T = 200000 kg m/s

=> T = (1000000/200000) s

=> T = 5 s

By putting the value of T in equation (1), we get

L/(5 s)^2 = 2 m/ s^2

=> L/(25 s^2) = 2 m/ s^2

=> L = 50 m

Now, by putting the value of L and T in equation (3) , we get

100 M (50m/5s) = 200000 kg m/s

=> M = 200 kg

Hope it will help you.