Answer

Verified

462k+ views

- Hint: To find the answer of this question we need to apply the concept of dimensional correctness of an equation. We can add or subtract two quantities only if the units of the two quantities are the same i.e. dimension of the quantities need to be the same. Applying this concept to the above equation we can find the dimension of the constant b.

For an equation to be correct, the equation should be dimensionally correct. i.e. the quantities on both sides of the equation should have the same dimension or the quantities related with each other by addition of subtraction should have the same dimension.

In the given equation we have in the left-hand side, we have that the constant b is related to V with subtraction. For this to be right the dimension of b should be the same as that of V.

Now, here, V is the volume of the gas. So, the dimension of constant b is equal to that of the dimension of volume.

Dimension of volume is given as $\left[ {{L}^{3}} \right]$

So, dimension of constant b will be $\left[ {{L}^{3}} \right]$

Note: We can also find the dimension of applying this concept.

Here, the dimension of $\dfrac{a}{{{V}^{2}}}$ will be the same as the dimension of P.

Now, dimension of P is $\left[ {{M}^{1}}{{L}^{-1}}{{T}^{-2}} \right]$

Dimension of V is $\left[ {{L}^{3}} \right]$

So, dimension of ${{V}^{2}}$ will be $\left[ {{L}^{6}} \right]$

So, dimension of a will be, $\left[ {{M}^{1}}{{L}^{-1}}{{T}^{-2}} \right]\times \left[ {{L}^{6}} \right]=\left[ {{M}^{1}}{{L}^{5}}{{T}^{-2}} \right]$

We also find the dimension by simplifying the given equation and then equating the dimension of each quantity related with addition and subtraction in both sides of the equation.

__Complete step-by-step solution__-For an equation to be correct, the equation should be dimensionally correct. i.e. the quantities on both sides of the equation should have the same dimension or the quantities related with each other by addition of subtraction should have the same dimension.

In the given equation we have in the left-hand side, we have that the constant b is related to V with subtraction. For this to be right the dimension of b should be the same as that of V.

Now, here, V is the volume of the gas. So, the dimension of constant b is equal to that of the dimension of volume.

Dimension of volume is given as $\left[ {{L}^{3}} \right]$

So, dimension of constant b will be $\left[ {{L}^{3}} \right]$

__The correct option is (C).__Note: We can also find the dimension of applying this concept.

Here, the dimension of $\dfrac{a}{{{V}^{2}}}$ will be the same as the dimension of P.

Now, dimension of P is $\left[ {{M}^{1}}{{L}^{-1}}{{T}^{-2}} \right]$

Dimension of V is $\left[ {{L}^{3}} \right]$

So, dimension of ${{V}^{2}}$ will be $\left[ {{L}^{6}} \right]$

So, dimension of a will be, $\left[ {{M}^{1}}{{L}^{-1}}{{T}^{-2}} \right]\times \left[ {{L}^{6}} \right]=\left[ {{M}^{1}}{{L}^{5}}{{T}^{-2}} \right]$

We also find the dimension by simplifying the given equation and then equating the dimension of each quantity related with addition and subtraction in both sides of the equation.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

How do you graph the function fx 4x class 9 maths CBSE

Which are the Top 10 Largest Countries of the World?

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

The largest tea producing country in the world is A class 10 social science CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE