Home
Class 11
PHYSICS
A small asteroid is orbiting around the ...

A small asteroid is orbiting around the sun in a circular orbit of radius `r_(0)` with speed `V_(0)`. A rocket is launched from the asteroid with speed `V = alpha V_(0)` , where V is the speed relative to the sun. The highest value of `alpha` for which the rocket will remain bound to the solar system is (ignoring gravity due to the asteroid and effects of other planets) –

A

`sqrt2`

B

2

C

`sqrt3`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Mechanical energy of asteroid `=1/2mV^2-(GMm)/(r_0)`

Rocket will remain bound to the solar system. If,
`-(GMm)/(r_0)+1/2mV^2=0rArr(GMm)/(r_0)=1/2mV^2rArr(GMm)/(r_0)`
`=1/2malpha^2V_0^2`
`mV_0^2=1/2malpha^2v_0^2rArralpha=sqrt2`
Promotional Banner

Similar Questions

Explore conceptually related problems

When a satellite going around the earth in a circular orbit of radius r and speed v loses some of its energy, then

What is the magnetic moment of an electron orbiting in a circular orbit of radius r with a speed v?

An electron moves in circular orbit of radius r with constant speed v.The force acting in it is

A satellite is revolving around the earth in a circular orbit of radius r with speed v. What will be the effect on speed f satellite if radius is decreased by 5% ?

Asteroids revolve around the sun between the orbits of the planets :

Magnetic moment of an electron of charge e moving in a circular orbit of radius r with speed v is given by

A satellite is moving around the earth's with speed v in a circular orbit of radius r . If the orbit radius is decreases by 1% , its speed will

The magnetic moment of an electron of charge e moving in a circular orbit of radius r with speed v is given by

The orbital speed of an electron orbiting around the nucleus in a circular orbit of radius r is v. Then the magnetic dipole moment of the electron will be