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In a certain system of absolute units th...

In a certain system of absolute units the acceleration produced by gravity in a body falling freely is denoted by `3`, the kinetic energy of a `272.1 kg` shot moving with velocity `448` metres per second is denoted by `100`, and its momentum by 10.
The unit of length is

A

15.36 m

B

153.6 m

C

68.57 m

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let unit of length, time and mass be `L_(1), T_(1)` and `M_(1)` respectively.
According to question
`9.8 LT^(-2) =3L_(1)T_(1)^(-2)`
`1/2 (272.1)(448)^(2) ML^(2)T^(-2)=100 M_(1)L_(1)^(2)T_(1)^(-2)`
`(272.1)(448) MLT^(-1)=10 M_(1)L_(1)T_(1)`
bu solving above equation `L_(1)=153.6 L`
`=153.6 m`
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