The Sun’s angular diameter is measured to be 1920′′. The distance D of the Sun from the Earth is $1.496\times {10}^{11}<mspace\; width="1em"></mspace>\mathrm{m}.$ The diameter of the Sun:

1.  $2.39\times {10}^9<mspace\; width="1em"></mspace>\mathrm{m}$

2.  $0.39\times {10}^9<mspace\; width="1em"></mspace>\mathrm{m}$

3.  $1.39\times {10}^9<mspace\; width="1em"></mspace>\mathrm{m}$

4.  $1.39\times {10}^{10}<mspace\; width="1em"></mspace>\mathrm{m}$

If the size of a nucleus (in the range of \(10^{-15}\) to \(10^{-14}\) m) is scaled up to the tip of a sharp pin, what roughly is the size of an atom? Assume tip of the pin to be in the range \(10^{-5}\) m to \(10^{-4}\) m.
1. \(1\) m
2. \(10\) m
3. \(10^{-10}\) m
4. \(10^{-5}\) m

Two clocks are being tested against a standard clock located in a national laboratory. At 12:00:00 noon by the standard clock, the readings of the two clocks are:

If you are doing an experiment that requires precision time interval measurements, which of the two clocks will you prefer?

We measure the period of oscillation of a simple pendulum. In successive measurements, the readings turn out to be \(2.63~\text s, 2.56~\text s, 2.42~\text s, 2.71~\text s,\) and \(2.80~\text s.\) The average absolute error and percentage error, respectively, are:
1. \(0.22~\text s\) and \(4\%\)
2. \(0.11~\text s\) and \(4\%\)
3. \(4~\text s\) and \(0.11\%\)
4. \(5~\text s\) and \(0.22\%\)

The temperatures of two bodies measured by a thermometer are \(t_1=20^\circ \text{C}\pm0.5^\circ \text{C}\) and \(t_2=50^\circ \text{C}\pm0.5^\circ \text{C}.\) The temperature difference with permissible error is:
1. \(31^\circ \text{C}\pm0.5^\circ \text{C}\)
2. \(30^\circ \text{C}\pm1.0^\circ \text{C}\)
3. \(30^\circ \text{C}\pm0.0^\circ \text{C}\)
4. \(30^\circ \text{C}\pm1.5^\circ \text{C}\)

The resistance \(R=\frac{V}{I}\) where \(V=(100 \pm 5) ~V\) and \(I=(10 \pm 0.2)~ A\). The percentage error in \(R\) is:
1. \(5\%\)
2. \(2\%\)
3. \(7\%\)
4. \(3\%\)

Two resistors of resistances ${\mathrm{R}}_1<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\left(100<mspace\; width="1em"></mspace>\pm <mspace\; width="1em"></mspace>3\right)$ ohm and $R_2<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\left(200<mspace\; width="1em"></mspace>\pm <mspace\; width="1em"></mspace>4\right)$ ohm are connected in series, the equivalent resistance of the series combination is:

1.  (300 ± 7) ohm

2.  (300 ± 1) ohm

3.  (300 ± 0) ohm

4.  (100 ± 1) ohm

Two resistors of resistances ${\mathrm{R}}_1<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\left(100<mspace\; width="1em"></mspace>\pm <mspace\; width="1em"></mspace>3\right)$ ohm and ${\mathrm{R}}_2<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\left(200<mspace\; width="1em"></mspace>\pm <mspace\; width="1em"></mspace>4\right)$ ohm are connected in parallel. The equivalent resistance of the parallel combination is:

1.  (300 ± 7) ohm

2.  (66.7 ± 7) ohm

3.  (66.7 ± 1.8) ohm

4.  (100 ± 1) ohm

The relative error in \(Z,\) if \(Z=\frac{A^{4}B^{1/3}}{CD^{3/2}}\) is:
1. \(\frac{\Delta A}{A}+\frac{\Delta B}{B}+\frac{\Delta C}{C}+\frac{\Delta D}{D}\)

2. \(4\frac{\Delta A}{A}+\frac{1}{3}\frac{\Delta B}{B}-\frac{\Delta C}{C}- \frac{3}{2}\frac{\Delta D}{D}\)

3. \(4\frac{\Delta A}{A}+\frac{1}{3}\frac{\Delta B}{B}+\frac{\Delta C}{C}+\frac{2}{3}\frac{\Delta D}{D}\)

4. \(4\frac{\Delta A}{A}+\frac{1}{3}\frac{\Delta B}{B}+\frac{\Delta C}{C}+\frac{3}{2}\frac{\Delta D}{D}\)

The period of oscillation of a simple pendulum is $\mathrm{T}<mspace\; width="1em"></mspace>=2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The percentage error in g is:

1.  $2\%$

2.  $3\%$

3.  $5\%$

4.  $0\%$