Question

Which among the following can be deduced using only dimensional method? (k is dimensionless constant) ​

Answer 1

The expression v= u + at can be deduced using only the dimensional method.

• Dimensional analysis is the method by which dimensions of an unknown variable are found by comparing its relationship with a known value.
• Dimensional Analysis can also be used to deduce formulae. However, it cannot be used to deduce formulae with constant values as they are dimensionless.

• In the given question,

1. 4mv² + mgh:

• In this expression, the term 4mv² cannot be deduced using dimensional analysis as it contains '4' which is dimensionless.
• Dimensionally, the formula will still be consistent without 4 so it cannot be deduced using only dimensional analysis.

2. asinωt + bsinωt

• In this part, we know that sin /cos of any angle is dimensionless.
• So it cannot be derived using only dimensional analysis.

3. v = u +at

• This expression does not have any constant/dimensionless values
• So by knowing the relation between velocity, acceleration and, time, we can deduce this formula by only dimensional analysis.

4. v = kat

• In this formula, it is given k is a dimensional constant, hence its value can only be calculated theoretically or experimentally.
• Thus this expression cannot be deduced only by dimensional analysis as we cannot find the exact value of k.

Thus, v = u +at can be deduced using only dimensional analysis.