Dimensional analysis cannot be used for:
1. deriving relations
2. deriving relation with four unknown variables
3. converting system of units
4. checking correctness of relations
Which of the following does not have the dimensions of force?
1. Potential gradient
2. Energy gradient
3. Weight
4. Rate of change of momentum
Which of the following measurements is the most precise?
1. 5.00 mm
2. 5.00 cm
3. 5.00 m
4. 5.00 km
Which of the following ratios express pressure?
1. Force/Volume
2. Energy/Volume
3. Energy/Area
4. Force/length
Choose the incorrect statement from the given ones:
| 1. | The volume of a cube of side \(1~\text{cm}\) is equal to \(10^{-6}~\text{m}^2\). |
| 2. | The surface area of a solid cylinder of radius \(2.0~\text{cm}\) and height \(10~\text{cm}\) is equal to \(1.5\times10^{4}~\text{mm}^2\). |
| 3. | A vehicle moving with a speed of \(18~\text{km/h}\) covers \(5~\text m\) in \(1~\text s\). |
| 4. | The relative density of lead is \(11.3\). Its density is \(11.3~\text{g/cm}^3\). |
Choose the incorrect statement from the given ones:
| 1. | \(1~\mathrm{kgm^2s^{-2}}=10^{7}~\mathrm{gcm^2s^{-2}}\) |
| 2. | \(1~\text m=1.057\times10^{-16}~\text{ly}\) |
| 3. | \(3.0~\mathrm{m/s^2}=10.8~\mathrm{km/h}\) |
| 4. | \(G=6.67\times10^{-11}~\mathrm{Nm^2/kg^2}=6.67\times10^{-6}~\mathrm{cm^3s^{-2}g^{-1}}\) |
A calorie is a unit of heat (energy in transit) and it equals about \(4.2~\text J\) where \(1~\text J = 1~\mathrm{kgm^{2}s^{–2}}.\) Suppose we employ a system of units in which the unit of mass equals \(\alpha~\text{kg},\) the unit of length equals \(\beta~\text{m}\), the unit of time is \(\gamma~\text{s}.\) What is the magnitude of a calorie in terms of the new units?
1. \(4.2\alpha^{–1}\beta^{–1}\gamma^2\)
2. \(4.2\alpha^{–2}\beta^{–2}\gamma^2\)
3. \(4.2\alpha^{–1}\beta^{–2}\gamma^2\)
4. \(4.2\alpha^{–1}\beta^{–2}\gamma^1\)
The statement “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison” emphasizes the importance of reference standards in physics. Which of the following revised statements correctly reflects this principle?
| 1. | Atoms are very small objects. |
| 2. | A jet plane moves with great speed. |
| 3. | The mass of Jupiter is very large. |
| 4. | A proton is about \(1836\) times more massive than an electron. |
A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes \(8~\text{min}\) and \(20~\text{s}\) to cover this distance?
1. \(125\)
2. \(250\)
3. \(350\)
4. \(500\)
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