In a new system of units called star units, 1 kg* = 10 kg , 1 m* =1 km and 1s* = 1 minute, what will be the value of 1J in the new system ?

Question

In a new system of units called star units, 1 kg* = 10 kg , 1 m* =1 km and 1s* = 1 minute, what will be the value of 1J in the new system ? (A)  2.4 × 10-5 J*  (B)  3.6 × 10-4 J*  (C)  4.2 × 10-3 J*  (D)  4.2 × 10-2 J*

Tardigrade Admin · Accepted Answer

Given that For star units 1kg* =10 kg 1m* = 1 km and 1s* = 1 m The value of 1 J in star units 1 J = 1 [ML2 T-2] = 1 [1 kg m2s-2] = [1× (1/10) kg + ((m*/1000))2 + ((s*/60))-1] = 3.6 × 154 J

Q. In a new system of units called star units, $1 k g^{} = 10 k g$ , $1 m^{} = 1 km$ and $1 s^{*} = 1$ minute, what will be the value of $1 J$ in the new system ?

$2.4 \times 1 0^{- 5} J^{*}$

$3.6 \times 1 0^{- 4} J^{*}$

$4.2 \times 1 0^{- 3} J^{*}$

$4.2 \times 1 0^{- 2} J^{*}$

Given that
For star units $1 k g^{} = 10 k g$
$1 m^{} = 1 km$
and $1 s^{} = 1 m$
The value of $1 J$ in star units
$1 J = 1 [M L^{2} T^{- 2}] = 1 [1 k g m^{2} s^{- 2}]$
$= [1 \times \frac{1}{10} k g + (\frac{m ^{}}{1000})^{2} + (\frac{s ^{*}}{60})^{- 1}]$
$= 3.6 \times 154 J$

Q. In a new system of units called star units, 1kg∗=10kg , 1m∗=1km and 1s∗=1 minute, what will be the value of 1J in the new system ?

2.4×10−5J∗

3.6×10−4J∗

4.2×10−3J∗

4.2×10−2J∗