In a new system of units, unit of mass is 10 kg , unit of length is 1 km and unit of time is 1 minute. The value of 1 joule in this new hypothetical system is

Question

In a new system of units, unit of mass is 10 kg , unit of length is 1 km and unit of time is 1 minute. The value of 1 joule in this new hypothetical system is (A) 3.6 × 10-4 new units (B) 6 × 107 new units (C) 1011 new units (D) 1.67 × 104 new units

Tardigrade Admin · Accepted Answer

The dimensional formula of energy is [ ML 2 T -2]. n2=1[(1 kg /10 kg )]1[(1 m /1 km )]2[(1 s /1 min )]-2 =(1/10) × (1/106) × (1/(60)-2) =(3600/107)=3.6 × 10-4

Q. In a new system of units, unit of mass is $10 k g,$ unit of length is $1 km$ and unit of time is 1 minute. The value of 1 joule in this new hypothetical system is

$3.6 \times 1 0^{- 4}$ new units

$6 \times 1 0^{7}$ new units

$1 0^{11}$ new units

$1.67 \times 1 0^{4}$ new units

The dimensional formula of energy is $[M L^{2} T^{- 2}]$ .
$n_{2} = 1 [\frac{1 k g}{10 k g}]^{1} [\frac{1 m}{1 km}]^{2} [\frac{1 s}{1 min}]^{- 2}$
$= \frac{1}{10} \times \frac{1}{1 0 ^{6}} \times \frac{1}{( 60 ) ^{- 2}}$
$= \frac{3600}{1 0 ^{7}} = 3.6 \times 1 0^{- 4}$

Q. In a new system of units, unit of mass is 10kg, unit of length is 1km and unit of time is 1 minute. The value of 1 joule in this new hypothetical system is

3.6×10−4 new units

6×107 new units

1011 new units

1.67×104 new units