Home
Class 12
PHYSICS
With what speed v(0) should a body be pr...

With what speed `v_(0)` should a body be projected as shown in the figure, with respect to a planet of mass `M` so that it would just be able to graze the planet and escape ? The radius of the planet is `R`. (Assume that the planet is fixed ).

Text Solution

Verified by Experts

By conservation of angular momentum we obtain
`mv_(0)d=mvr`
`impliesv=(mv_(0)d)/(mr)=v_(0)(d//r)`
By conservation of energy at `A` and `B`, we have
`(1)/(2)mv_(0)^(2)-(GMm)/(sqrt(D^(2)+d^(2)))=(1)/(2)mv^(2)-(GMm)/(r )`
When `r~~R` we obtain,
`(1)/(2)mv_(0)^(2)-(GMm)/(sqrt(D^(2)+d^(2)))-(1)/(2)m.(v_(0)^(2)d^(2))/(R^(2))-(GMm)/(R )`
`(1)/(2)mv_(0)^(2)((d^(2))/(R^(2))-1)=GMm[(1)/(R )-(1)/(sqrt(D^(2)+d^(2)))]`
`impliesv_(0)=sqrt((2GM((1)/(R )-(1)/(sqrt(D^(2)+d^(2)))))/(((d^(2))/(R^(2))-1)))`
Promotional Banner

Similar Questions

Explore conceptually related problems

If potential at the surface of a planet is taken as zero, the potential at infinty will be ( M and R are mass of radius of the planet)

A planet has mass equal to mass of the earth but radius one fourth of radius of the earth . Then escape velocity at the surface of this planet will be

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to 1/3rd the escape velocity for the planet. The maximum height attained by the body is

The surface temperature of the sun is T_(0) and it is at average distance d from a planet. The radius of the sun is R . The temperature at which planet radiates the energy is

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is 9 : 4 . The mass of the planet is (1)/(9) th of that of the Earth, what is the radius of the planet ? (Tale the planets to have the same mass density).

What will be the orbital speed from a planet of mass 10^(30) kg and and of radius 10^(8) m ?

A body of mass 500 g is thrown upwards with a velocity 20 ms^-1 and reaches back to the surface of a planet after 20 sec . Then the weight of the body on that planet is (Assume g to be constant) xN. Find x.

The ratio of the weight of a body on the Earth’s surface to that on the surface of a planet is 9 : 4. The mass of the planet is 1/9 of that of the Earth. If ‘R’ is the radius of the Earth, then the radius of the planet is where n is ___________ . (Take the planets to have the same mass density)