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**JEE Mains**

__Single Choice Type__Two metal spheres of the same material and radius $r$ are in contact with each other. The gravitational force of attraction between the spheres is given by:

From a sphere of mass $M$ and radius $R$, a smaller sphere of radius $2R $ is carved out such that the cavity made in the original sphere is between its centre and the periphery. (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is $3R$, the gravitational force between the two spheres is :

A particle is moving with speed $v=bx $ along positive x-axis. Calculate the speed of the particle at time $t=τ$ (assume that the particle is at origin at $t=0$)

The position of a particle as a function of time t, is given by $x(t)=at+bt_{2}−ct_{3}$ where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be?

A satellite is seen after each $8h$ over the equator at a place on the earth when its sense of rotation is opposite to the earth. The time interval after which it can be seen at the same place when the sense of rotation of the earth and the satellite is the same will be

Two satellites are revolving round the earth at different heights. The ratio of their orbital speeds is $2:1$. If one of them is at a height of $100km$, the height of the other satellite is $($Radius of earth $R=6400$ km $)$

An object is projected vertically upwards from the surface of the earth with a velocity $3$ times the escape velocity $v_{e}$ from earth's surface. What will be its final velocity after escape from the earth's gravitational pull?