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### Dimensional analysis practice worksheet

This post is about Dimensional analysis practice worksheet practice these problems and try to solve them in one hour.

Question 1 The parallax of a heavenly body measured from two points diametrically opposite on the equator of the earth is 1.0 minute. If the radius of the earth is 6400 Km, find the distance of heavenly body from the center of the earth in AU. Take 1AU=1.5×1011m.
Question 2 A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the gauge arbitrarily by increasing the number of divisions on the circular scale?
Question 3 Assuming that the frequency ($\nu$) of the vibrating string depends upon the load (F) applied , length of the string (l) and mass per unit length (m), prove that
$\nu = \frac{1}{2l} \sqrt{\frac{F}{m}}$
Question 4 What are the dimensions of
(a) gravitational constant
(b) work
(c) angular velocity
(d) pressure
Question 5 Write the dimensions of a/b in the relation
$F=a\sqrt{x}+bt^{2}$
Where F is force, x is distance and t is time.
Question 6 Check the correctness of the relation
$\rho =\frac{3g}{4\pi rG}$
Where symbols have usual meaning.
Question 7 The coefficient of viscosity ($\eta$) of a gas depends upon mass m, the effective diameter d, and mean speed v of the gas molecules. Use dimensional analysis to find the relation between them.
Question 8 The potential difference of V=20±1 Volt , when applied across a resistance gives a current of 2.5±0.5 ampere. Find the resistance with limits of error.
Question 9 Convert 4.29 light years into parsecs. Calculate the parallax of a star at the distance when viewed from two locations of earth six months apart in its orbit around the sun.
Question 10 In an experiment, on determining the density of a rectangular block, the dimensions of the block are measured with a Vernier calipers (with a least count of 0.01 cm) and its mass is measured with a beam balance of least count of 0.1 g. How do we report our result for the density of the block.
Question 11 It is required to find the volume of a rectangular block. A Vernier calipers is used to measure the length, width and height of the block. The measured values are  1.37 cm, 4.11 cm, and 2.56 cm respectively.

Question 1 What is relative error or percentage error?
Question 2 What is Parallax error?

Question 3 How errors are propagated or combined?