Using rules of significant figures what is the value of \(22.8\text{ m} \times 3.4\text{ m}\):
The multiplication result must be rounded to the least number of significant figures among the measured values. Since 3.4 has only 2 significant figures, the result \(77.52\text{ m}^2\) is rounded to 2 significant figures, which is \(78\text{ m}^2\).
Convert \(25\text{ dyne}\) to a system where fundamental units of mass, length & time are \(100\text{ g}\), \(100\text{ cm}\) and \(1\text{ hour}\):
Using \(n_2 = n_1 [M_1/M_2]^1 [L_1/L_2]^1 [T_1/T_2]^{-2}\), we get \(n_2 = 25 \left(\frac{1}{100}\right) \left(\frac{1}{100}\right) \left(\frac{1}{3600}\right)^{-2} = 32400\).
Assertion (A): Mass, length and time may be taken as fundamental quantities.
Reason (R): Mass, length and time are independent of one another.
Mass, length, and time are chosen as fundamental quantities because they are independent of each other and cannot be defined in terms of one another.
Assertion (A): eV and joule are the S.I. units of energy used in modern physics and mechanics respectively.
Reason (R): Different types of energies require different units in S.I. units.
The SI unit of all forms of energy is the joule. Electron-volt (eV) is not an SI unit, and different forms of energy do not require different SI units.
If \(x = at + bt^2\), where \(x\) is the distance travelled by the body in kilometres while \(t\) is the time in seconds, then the units of \(b\) is:
[1989]
By homogeneity, \([bt^2] = [x]\). So \([b] = [x]/[t^2] = km/s^2\).
Plane angle and solid angle have:
[2022]
Plane angle (radian) and solid angle (steradian) are dimensionless quantities (ratios of lengths or areas) but possess units.
Which of the following statement is not true?
Pressure is defined as force per unit area, where the force is perpendicular to the surface. Since it acts equally in all directions, pressure is a scalar quantity.