Question

in a book, the answer for a particular question is expressed as b = ma/k [√1 + 2kl/ma] here m represents mass, a represents acceleration , l represents length. The unit of b should be​

Answer 1

Given that,

The quantity is given by :

$b=\dfrac{ma}{k}[\sqrt{1+\dfrac{2kl}{ma}}]$

Here

m is mass

a is acceleration

To find,

The unit of b.

Solution,

When $\dfrac{2kl}{ma}$ is added to 1, it becomes dimensionless. So,

$\dfrac{2kl}{ma}=1\\\\k=\dfrac{ma}{2l}$

Putting SI units of m, a and l we get the unit of k as :

$k=\dfrac{kg\times ms^{-2} }{2\times m}\\\\k=kg/s^2$

The given formula becomes :

$b=\dfrac{ma}{k}[\sqrt{1+\dfrac{2kl}{ma}}]\\\\b=\dfrac{kg-m/s^2}{kg/s^2}\\\\b=m$

So, the unit of b is meters.

Learn more,

SI units

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Answer 2

Answer: Unit of b = m (metres)

Explanation:

Given expression:

b = ma/k[√(1 + 2kl/ma)]

where, m = mass, a = acc, l = length.

Now,

kb = ma√(1 + 2kl/ma)

By squaring both sides, we get:

k²b² = m²a² × (ma + 2kl)/ma

=> k²b² = ma(ma + 2kl)

=> k²b² = m²a² + 2makl

=> k²b² - m²a² - 2makl = 0.

(Do not consider k as unitless or dimensionless until it has been mentioned.)

By principle of homogeneity,

Unit/dimension of k²b² = Unit/dim of m²a² = Unit/dim of 2makl.

(Regardless of the symbols. First step is to know the units of k.)

Consider 2makl = m²a²

=> k = ma/2l = ma/l (2 = no units)

=> k = kg . ms-² × m-¹ = kg.s-²

Now, k²b² = 2makl

=> b = √(2makl/k²) = √[(kg . ms-² . m)/kgs-²]

=> b = √m² = m.

Therefore, b = metres.