Question : In a new unit system, 1 unit of time is equal to 10 seconds, 1 unit of mass is 5 kg and 1 unit of length is 20 m. In the new system of units, 1 unit of energy is equal to:
(A) 20 Joule
(B) 1/20 Joule
(C) 4 Joule
(D) 16 Joule
Doubt by Divya
Solution :
1 unit of time = 10 seconds
1 unit of mass = 5 kg
1 unit of length = 20 m
The traditional method of solving this question by using the formula n2=n1[M1/M2]^a[L1/L2]^b[T1/T2]^c is already known to us.
But since this is an MCQ Question so we will solve it by using some short method
We know
Kinetic Energy = 1/2 mv²
Kinetic Energy = 1/2 [Mass][Length/Time]²
Kinetic Energy = 1/2 [Mass][Length/Time]²
1 new unit of energy
=1 unit mass × (1 unit length)²/(1 unit time)²
=1 unit mass × (1 unit length)²/(1 unit time)²
=5kg × (20 m)²/(10 sec)²
=[5×400]/100
=20 kgm²/s²
=20 J
=[5×400]/100
=20 kgm²/s²
=20 J
Hence, 1 new unit of energy = 20 J
So, (A) 20 Joule, would be the correct option.