In this page we have *Dimensional analysis worksheet* . Hope you like them and do not forget to like , social share
and comment at the end of the page.

**Question 1** Show that expression $v={{v}_{0}}+at$ is dimensionally correct, where $v$and ${{v}_{0}}$ represent velocities and $a$ is acceleration and $t$ represents time.

**Question 2** Each of the following equations was given by a student during an examination.

Do the dimensional analysis of each equation and explain why the equations cannot be correct.

**Question 3 **Suppose that the displacement of an object is related to time according to the expression$x=B{{t}^{2}}$ . What are the dimensions of$B$?

**Question 4** Find the SI unit of pressure.

**Question 5 **(a) Is it possible for two quantities to have the same dimensions but different units.

(b) Is it possible for two quantities to have same units but different dimensions?

**Question 6** Suppose we are told that the acceleration

*‘a’* of a particle moving with uniform speed

*‘v’* in a circle of radius

*‘r’* is proportional to some power of

*r*, say

*r*^{n}, and some power of

*v*^{m}. How can we determine the value of

*n* and

*m*.

**Question 7** The mass of a solid cube is 856 g, and each edge has a length of 5.35 cm. Determine the density $\rho $ of the cube in basic SI units.

**Question 8** The period

*‘T’* of a simple pendulum is measured in time units and is described by

\[T=2\pi \sqrt{\frac{l}{g}}\]
Where

*l* is the length of the pendulum and ‘g’ is the free fall acceleration in units of length divided by square of time. Show that this equation is dimensionally correct.

**Question 9** Estimate the average mass density of a sodium atom assuming its size to be about 2.5 Å. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the density of sodium in its crystalline phase: 970 kg m

^{-3}. Are the two densities of the same order of magnitude? If so, why?

**Question 10** In the following

*x *is in meters,

*t* in seconds,

* v* in m/s and

*a* is in m/s

^{2}. Find the SI unit of each combination.

a) $\frac{{{v}^{2}}}{xa}$

b) $\sqrt{\frac{x}{a}}$

c) $\frac{1}{2}at^2$

**Download Dimensional analysis worksheet as pdf **

**link to this page by copying the following text**

**Note to our visitors :-**
Thanks for visiting our website. From feedback of our visitors we came to know that sometimes you are not able to see the answers given under "Answers" tab below questions. This might happen sometimes as we use javascript there. So you can view answers where they are available by reloding the page and letting it reload properly by waiting few more seconds before clicking the button.

We really do hope that this resolve the issue. If you still hare facing problems then feel free to contact us using feedback button or contact us directly by sending is an email at **[email protected]**

We are aware that our users want answers to all the questions in the website. Since ours is more or less a one man army we are working towards providing answers to questions available at our website.

Class 11 Maths
Class 11 Physics
Class 11 Chemistry