Question : Velocity v and acceleration a in two systems of units 1 and 2 are related as v2=nv1/m2 and a2=a1/mn, respectively. Here m and n are constants. The relations for distance and time in two systems respectively are :
[JEE 2022, 28th June Shift-II]
Doubt by Navya
Solution :
v2=nv1/m2 (Given)
v2/v1=n/m2 — (1)
a2=a1/mn (Given)
a2/a1=1/mn
(v2/t2)/(v1/t1) = 1/mn
(v2/v1)×(t1/t2) = 1/mn
(n/m2)×(t1/t2)=1/mn [Using equation (1)]
t1/t2=m2/mn2
t1/t2=m/n2
(n2/m)t1=t2
t1/t2=m/n2
Now,
Using Equation (1)
v2/v1=n/m2
(l2/t2)/(l1/t1)=n/m
(l2/l1)×(t1/t2)=n/m2
(l2/l1)×(m/n2)=n/m2
(l2/l1)=n3/m3
(n3/m3)l1=l2
Hence, a) would be the correct option.