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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

A
13,13
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B
12,12
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C
14,14
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D
15,15
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Solution

## The correct option is B 12,12Dimensional formula of speed v, [v]=[M0LT−1] Dimensional formula of acceleration due to gravity g, [g]=[M0LT−2] Dimensional formula of distance travelled h, [h]=[M0LT0] As, v∝gphq ⇒v=kgphq where k is proportionality constant ⇒[M0LT−1]=[(M0LT−2]p×[M0LT0]q ⇒[M0LT−1]=[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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