The mass density of a spherical body is given by $\rho \left(r\right)=\frac{k}{r}$ for $r\le R$ and $\rho \left(r\right)=0$ for $r>R,$ where $r$ is the distance from the center. The correct graph that describes qualitatively the acceleration, $a$ of a test particle as a function of $r$ is:

A very long (length $L$) cylindrical galaxy is made of uniformly distributed mass and has radius $R (R<<L)$. A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of the star is $T$ and its distance from the galaxy's axis is $r$, then

India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at $E$ and meets Mars at $M$. If the semi-major axis of Earth's orbit is ${\text{a}}_{\text{e}}=\text{1.5}\times 10^{11}\text{m}$ , that of Mar's orbit ${\text{a}}_{\text{m}}=\text{2.28}\times 10^{11}\text{m}$, taking Kepler's laws, give the estimate of time for Mangalyan to reach Mars from Earth.