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Question

The speed of a freely falling body from rest is proportional to gphq, where g is acceleration due to gravity and h is the distance travelled. The values of p and q are
  1. 14,14
  2. 15,15
  3. 13,13
  4. 12,12


Solution

The correct option is D 12,12
Dimensional formula of speed v,
[v]=[M0LT1]
Dimensional formula of acceleration due to gravity g,
[g]=[M0LT2]
Dimensional formula of distance travelled h,
[h]=[M0LT0]
As, vgphq
v=kgphq
where k is proportionality constant
[M0LT1]=[(M0LT2]p×[M0LT0]q
[M0LT1]=[M(0+0)L(p+q)T(2p+0)]
On comparing, we get,
p+q=1 and 2p=1 
So, p=12, putting this in p+q=1, we get q=12

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