‘Gulab Jamuns’ (assumed to be spherical) are to be heated in an oven. They are available in two sizes, one twice bigger (in radius) than the other. Pizzas (assumed to be discs) are also to be heated in oven. They are also in two sizes, one twice big (in radius) than the other. All four are put together to be heated to oven temperature. Choose the correct option from the following:

To determine the order in which the objects are heated to the oven temperature, we analyze the rate of heat transfer and temperature rise using basic thermodynamic principles.

When an object is placed in an oven, the rate of heat transfer into the object by convection and radiation at its surface is proportional to its surface area (A). Let the heat transfer rate be denoted by Q:
$Q\propto A$

The amount of heat required to raise the temperature of the object to the oven temperature is proportional to its mass (m), which is in turn proportional to its volume (V) assuming constant density (ρ) and specific heat capacity (c):
$Q_{\text{required}}\propto m\propto V$

The time (t) taken to heat the object is proportional to the ratio of the required heat to the rate of heat transfer:
$t\propto \frac{Q_{\text{required}}}{Q}\propto \frac{V}{A}$

Let us analyze this ratio for both the spherical gulab jamuns and the disc-shaped pizzas:

1. Spherical Gulab Jamuns:
For a sphere of radius R, the volume is:
$V=\frac{4}{3}\pi R^3$
And the surface area is:
$A=4\pi R^2$
Thus, the volume-to-area ratio is:
$\frac{V}{A}=\frac{\frac{4}{3}\pi R^3}{4\pi R^2}=\frac{R}{3}$
Since $t\propto R$, the heating time is directly proportional to the radius. Therefore, the smaller gulab jamun (with smaller radius R) will heat up faster than the larger one.

2. Disc-shaped Pizzas:
For a disc of radius R and thickness d (where d is constant for both sizes of pizzas), the volume is:
$V=\pi R^{2}d$
The heat-receiving surface area (top and bottom faces primarily, neglecting the thin edge) is:
$A\approx 2\pi R^2$
Thus, the volume-to-area ratio is:
$\frac{V}{A}\approx \frac{\pi R^{2}d}{2\pi R^2}=\frac{d}{2}$
Because the thickness d is constant, the ratio $\frac{V}{A}$ is independent of the radius R. Consequently, both sizes of pizzas will heat up in approximately the same amount of time.

Combining these findings, we conclude that the smaller gulab jamuns will be heated before the bigger ones, while the two sizes of pizzas will heat at roughly the same time. This matches the correct option.

Therefore, the correct option is: Smaller gulab jamuns are heated before bigger ones.