$A$ body of mass $m$ is moving in a circular orbit of radius $R$ about a planet of mass $M$. At some instant,it splits into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2}$,and the other mass moves in a circular orbit of radius $\frac{3R}{2}$. The difference between the final and initial total energies is
- A$ - \frac{GMm}{2R}$
- B$ + \frac{GMm}{6R}$
- C$ - \frac{GMm}{6R}$
- D$ \frac{GMm}{2R}$
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Similar Questions
State whether the following statements are true or false:
$(a)$ The value of '$g$' is slightly less at the poles than at the equator.
$(b)$ The unit $\text{Newton/kilogram}$ $(N/kg)$ is also a unit of acceleration due to gravity.
$(c)$ The escape velocity $v_e$ for a stationary object on the surface of a planet is directly proportional to the mass and radius of the planet.
$(a)$ The value of '$g$' is slightly less at the poles than at the equator.
$(b)$ The unit $\text{Newton/kilogram}$ $(N/kg)$ is also a unit of acceleration due to gravity.
$(c)$ The escape velocity $v_e$ for a stationary object on the surface of a planet is directly proportional to the mass and radius of the planet.
Easy
View SolutionThree equal masses of $m \; kg$ each are fixed at the vertices of an equilateral triangle $ABC.$
$(a)$ What is the force acting on a mass $2 \; m$ placed at the centroid $G$ of the triangle?
$(b)$ What is the force if the mass at the vertex $A$ is doubled?
Take $AG = BG = CG = 1 \; m$.
$(a)$ What is the force acting on a mass $2 \; m$ placed at the centroid $G$ of the triangle?
$(b)$ What is the force if the mass at the vertex $A$ is doubled?
Take $AG = BG = CG = 1 \; m$.
Medium
View Solution$A$ particle of mass $M$ is situated at the centre of a spherical shell of same mass $M$ and radius $a$. The gravitational potential at a point situated at a distance of $\frac{a}{2}$ from the centre will be:
Medium
View SolutionTwo identical particles of mass $1 \, kg$ each go round a circle of radius $R$,under the action of their mutual gravitational attraction. The angular speed of each particle is:
Match the $\text{LIST-I}$ with $\text{LIST-II}$:
$\text{LIST-I}$ $\text{LIST-II}$ $A$. Gravitational constant $I$. $[LT^{-2}]$ $B$. Gravitational potential energy $II$. $[L^2 T^{-2}]$ $C$. Gravitational potential $III$. $[ML^2 T^{-2}]$ $D$. Acceleration due to gravity $IV$. $[M^{-1} L^3 T^{-2}]$
Choose the correct answer from the options given below:
| $\text{LIST-I}$ | $\text{LIST-II}$ |
|---|---|
| $A$. Gravitational constant | $I$. $[LT^{-2}]$ |
| $B$. Gravitational potential energy | $II$. $[L^2 T^{-2}]$ |
| $C$. Gravitational potential | $III$. $[ML^2 T^{-2}]$ |
| $D$. Acceleration due to gravity | $IV$. $[M^{-1} L^3 T^{-2}]$ |
Choose the correct answer from the options given below:
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