Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.
Reason (R): For a central force field the angular momentum is a constant.
In the light of the above statements, choose the most appropriate answer from the options given below:
An object is kept at rest at a distance of $3 R$ above the earth's surface where $R$ is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is : (Assume $\mathrm{M}=$ mass of earth, $\mathrm{G}=$ Universal gravitational constant)
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$
Assertion A: The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\frac{1}{2} \mathrm{mgR}$, where R is the radius of earth.
Reason R: The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
In the light of the above statements, choose the correct answer from the options given below
$$ \text { Match the LIST-I with LIST-II } $$
List - I |
List - II |
||
---|---|---|---|
A. | $$ \text { Gravitational constant } $$ |
I. | $$ \left[\mathrm{LT}^{-2}\right] $$ |
B. | $$ \text { Gravitational potential energy } $$ |
II. | $$ \left[\mathrm{L}^2 \mathrm{~T}^{-2}\right] $$ |
C. | $$ \text { Gravitational potential } $$ |
III. | $$ \left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right] $$ |
D. | $$ \text { Acceleration due to gravity } $$ |
IV. | $$ \left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right] $$ |