The SI unit of energy is \(J = kg m^{2} s^{-2}\text{;}\) that of speed v is \(m s^{-1}\) and of acceleration a is \(m s^{-2}\text{.}\) Which of the formulae for kinetic energy (K) given below can you rule out on the basis of dimensional arguments (m stands for the mass of the body):
\(\displaystyle K = m^{2}v^{3}\)
\(\displaystyle K = (1/2)mv^{2}\)
\(\displaystyle K = ma\)
\(\displaystyle K = (3/16)mv^{2}t\)
\(\displaystyle K = (1/2)mv^{2}+ ma\)
2.
Each side of a cube is measured to be 7.203 m. What are the total surface area and the volume of the cube to appropriate significant figures?
3.
Write the sum of the numbers 362.50, 273.2, and 0.502 in a proper significant figures.
4.
Round off the numbers 2.572, 2.566, and 2.725 to the three significant figures.
5.
Which of the following pair of physical quantities does not have same dimensional formula.
\(\frac{a}{V^{2}}\) has the same dimension as of P, and b has the same dimension as V.
7.
Round the following numbers:
62.5347 to four significant figures.
3.78721 to three significant figures.
23.55 to the 0.1 place.
\(2.16347 \times 10^{5}\) to four significant figures.
0.4203 to the nearest 0.01 place.
56.912 to the nearest whole number.
Answer.
57
8.
Write the answer for each expression using scientific notation with the appropriate number of significant figures.
\(\displaystyle 217 \div 903\)
\(\displaystyle 38.65 \times 105.74\)
\(\displaystyle 125 \times 9.000\)
\(2.16347 \times 10^{5}\) to four significant figures.
\(\displaystyle 13.77 + 908.226 +515\)
\(\displaystyle 255.0-99\)
\(\displaystyle 0.00666 \times 321\)
9.
Convert 1 light year into kilometer.
10.
Convert 1 \(gram/ml\) into \(kg/m^{3}\text{.}\)
11.
Find the time taken by the light to reach to us if it is coming from a distant galaxy of \(10^{25}\) m away.
12.
Moon makes \(0.5^{o}\) angular diameter if seen from the earth and earth makes \(2^{o}\) angular diameter if seen from the moon. What must be their relative size.
