Question 1:
easyUsing 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 \(78\text{ m}^2\).
Question 2:
easyConvert \(25\text{ dyne}\) 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 \(n_2 = 25 \left(\frac{1}{100}\right) \left(\frac{1}{100}\right) \left(\frac{1}{3600}\right)^{-2} = 32400\).
Question 3:
easyAssertion (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.
Question 4:
easyAssertion (A): eV and joule are the S.I. units of energy used in modern physics and mechanics respectively.
Reason (R):Â 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.
Question 5:
moderateThe angle \(1’\) (minute of arc) in radian is nearly equal to,
[2020- Covid]
Convert \(1'\) to degrees, then to radians. \(1' = (1/60)^\circ = (1/60) \times (\pi/180)\text{ rad} \approx 2.91 \times 10^{-4}\text{ rad}\)
Question 6:
moderateThe unit of thermal conductivity is
[2019]
Thermal conductivity \(k\) relates heat flux to temperature gradient. So, \(k\) has units of \(W/(m \cdot K) = W m^{-1} K^{-1}\).
Question 7:
moderateThe damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are:
[2012 pre]
Damping force \(F_d = -bv\). The constant \(b\) has dimensions \([F_d]/[v] = (MLT^{-2})/(LT^{-1}) = MT^{-1}\), which is \(kg s^{-1}\).
Question 8:
moderateThe density of a material in CGS system of units is \(4\text{ g/cm}^3\). In a system of units in which unit of length is \(10\text{ cm}\) and unit of mass is \(100\text{ g}\), the value of density of material will be:
[2011 Mains]
Given \(\rho = 4\text{ g/cm}^3\). New mass unit \(M' = 100\text{ g}\) and new length unit \(L' = 10\text{ cm}\). \(\rho = 4 \frac{1/100 M'}{(1/10 L')^3} = 4 \frac{1/100}{1/1000} \frac{M'}{L'^3} = 40 \frac{M'}{L'^3}\).
Question 9:
easyIf \(x = at + bt^2\), 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 \([b] = [x]/[t^2] = km/s^2\).
Question 10:
easyPlane angle and solid angle have:
[2022]
Plane angle (radian) and solid angle (steradian) are dimensionless quantities (ratios of lengths or areas) but possess units.