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. \(500\)
A student measures the thickness of a human hair by looking at it through a microscope of magnification \(100.\) He makes \(20\) observations and finds that the average width of the hair in the field of view of the microscope is \(3.5~\text{mm}.\) What is the estimate of the thickness of the hair?
1. \(0.0035~\text{mm}\)
2. \(0.0350~\text{mm}\)
3. \(0.1350~\text{mm}\)
4. \(0.2350~\text{mm}\)
Consider the following statements:
| (A) | The diameter of a thread is so small that it cannot be measured using a meter scale. |
| (B) | In a screw gauge the least count decreases on increasing the number of divisions on the circular scale. |
| (C) | A large number of observations (say, 100) will give more reliable results than a smaller number of observations (say, 5). |
Choose the correct option from the given ones:
| 1. | Only statements 1 and 2 are correct |
| 2. | Only statements 2 and 3 are correct |
| 3. | All three statements are correct |
| 4. | Only statements 1 and 3 are correct |
The photograph of a house occupies an area of \(1.75~\text{cm}^2\) on a \(35~\text{mm}\)35 mm slide. The slide is projected onto a screen, and the area of the house on the screen is \(1.55~\text{m}^2.\) What is the linear magnification of the projector-screen arrangement?
1. \(84.1\)
2. \(94.1\)
3. \(74.1\)
4. \(14.1\)
How many significant figures are in \(0.0006032~\text{m}^2?\)
1. \(8\)
2. \(4\)
3. \(9\)
4. none of these
The sum of the numbers \(436.32,227.2,\) and \(0.301\) in the appropriate significant figures is:
| 1. | \( 663.821 \) | 2. | \( 664 \) |
| 3. | \( 663.8 \) | 4. | \(663.82\) |
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