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Question

Position of a body with acceleration a is given by x=kam tn, here t is time. Find dimension of m and n.

A
m=2,n=1
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B
m=1,n=1
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C
m=2,n=2
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D
m=1,n=2
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Solution

The correct option is D m=1,n=2
x=Kamtn (i)

Where,

K=constant

Dimension of a=[LT2]

Dimension of x=[L]

Dimension of t=[T]

By putting all dimensions in equation (i) we get

[M0L1T0]=[M0L1T2]m[M0L0T1]n

Comparing the quantities we get,

m=1 (ii)

2m+n=0 (iii)

By putting the value of m=1 in equation (iii) we get,

2(1)+n=0

n=2

Dimension of m & n are 1, 2


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