NEET Questions

A particle of mass $m$ moves under the influence of a central force given by $F(r) = -k/r^3$. If the particle's orbit is circular with radius $r_0$, its time period of revolution is:

A particle of mass $m$ moves along a trajectory given by $\vec{r}(t) = (t - \sin(t))\hat{i} + (1 - \cos(t))\hat{j}$, where $t$ is time. The net force acting on the particle is:

A particle of mass 'm' moves under the influence of a central force given by $F(r) = -\frac{k}{r^3}$, where 'k' is a positive constant. If the particle's initial velocity is 'v' at a distance 'r' from the center of the force, what is the minimum velocity required for the particle to escape to infinity?

A particle of mass $m$ moves in a circular orbit of radius $r$ under the influence of a central force whose potential energy is given by $U(r) = kr^3$, where $k$ is a constant. The angular momentum of the particle is:

What does not change in the field of central force

A body moves in a circular orbit of radius $r$ under the action of a central force. Potential due to the central force is given by $V(r)$ – $kr$ ($k$ is a positive constant). Period of revolution of the body is proportional to:

Statement-1: The angular momentum under a central force is constant.Statement-2: A force directed towards a fixed point following inverse square law is conservative

Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e. $F \propto \frac{1}{r^3}$, but still remaining a central force. Then

A body of mass $2 \mathrm{~kg}$ is moving under the influence of a central force whose potential energy is given by $U=2 r^3 \mathrm{~J}$. If the body is moving in a circular orbit of $5 \mathrm{~m}$, its energy will be

Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon