The position of an object having mass 0.1 kg as a function of time $t$ is given as

$\vec{r} = \left( 10 t^2 \hat{i} + 5 t^3 \hat{j} \right)$ m. At $t = 1$ s, which of the following statements are correct?

A. The linear momentum $\vec{p} = \left( 2 \hat{i} + 1.5 \hat{j} \right)$ kg·m/s.

B. The force acting on the object $\vec{F} = \left( 2 \hat{i} + 3 \hat{j} \right)$ N.

C. The angular momentum of the object about its origin $\vec{L} = 15 \hat{k}$ J·s.

D. The torque acting on the object about its origin $\vec{\tau} = 20 \hat{k}$ N·m.

Choose the correct answer from the options given below:

A planet ($P_1$) is moving around the star of mass $2M$ in the orbit of radius $R$. Another planet ($P_2$) is moving around another star of mass $4M$ in a orbit of radius $2R$. Ratio of time periods of revolution of $P_2$ and $P_1$ is ________.

A particle is rotating in a circular path and at any instant its motion can be described as

$\theta = \frac{5t^4}{40} - \frac{t^3}{3}$.

The angular acceleration of the particle after 10 seconds is _________ rad/s².

A parallel plate air capacitor has a capacitance $C$. When it is half filled as shown in figure with a dielectric constant $K = 5$, the percentage increase in the capacitance is ________.