A student measured the diameter of a small steel ball using a screw gauge of least count \(0.001\) cm. The main scale reading is \(5\) mm and zero of circular scale division coincides with \(25\) divisions above the reference level. If the screw gauge has a zero error of \(-0.004\) cm, the correct diameter of the ball is:
1. \(0.521\) cm
2. \(0.525\) cm
3. \(0.053\) cm
4. \(0.529\) cm

A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^2}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}}$is [c is the velocity of light, G is the universal constant of gravitation and e is charge]:

1. $c^2{\left[G\frac{e^2}{4\pi {\epsilon }_0}\right]}^{\frac{1}{2}}$

2. $\frac{1}{c^2}{\left[\frac{e^2}{4G\pi {\epsilon }_0}\right]}^{\frac{1}{2}}$

3. $\frac{1}{c}G\frac{e^2}{4\pi {\epsilon }_0}$

4. $\frac{1}{c^2}{\left[G\frac{e^2}{4\pi {\epsilon }_0}\right]}^{\frac{1}{2}}$

Planck's constant (\(h\)), speed of light in the vacuum (\(c\)), and Newton's gravitational constant (\(G\)) are three fundamental constants. Which of the following combinations of these has the dimension of length?
1. \(\frac{\sqrt{hG}}{c^{3/2}}\)
2. \(\frac{\sqrt{hG}}{c^{5/2}}\)
3. \(\frac{\sqrt{hG}}{G}\)
4. \(\frac{\sqrt{Gc}}{h^{3/2}}\)