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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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Knowledge Check

  • n a certain system of absoulte units the acceleration produced by gravity in a body falling freely is denoted by 5, the kinetic energy of a 500 kg shot moving with velocity 400 metres per second is denoted by 2000 & its momentum by 100 The unit of mass is :-

    A
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    B
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    C
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    D
    1200 kg

  • Calculate the kinetic energy of a body of mass 2 kg moving with a velocity of 0.1 meter per second.

    A
    0.01 J
    B
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    C
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    D
    0.04 J

  • 1 joule of energy is to be converted into new system of units in which length is measured in 10 metre, mass in 10 kg and time in 1 minute. The numerical value of 1 J in the new system is :-

    A
    `36xx10^(-4)`
    B
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    C
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    D
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