A body is projected with a velocity equal to twice the escape velocity `(v_(e))` from the surface of the earth. With what velocity it will travel in i

Question

A body is projected with a velocity equal to twice the escape velocity `(v_(e))` from the surface of the earth. With what velocity it will travel in i

A body is projected with a velocity equal to twice the escape velocity `(v_(e))` from the surface of the earth. With what velocity it will travel in interplanetary space?
A. `sqrt(3GM)/( R)`
B. `sqrt(6GM)/( R)`
C. `sqrt(5GM)/( R)`
D. `sqrt(GM)/( R)`

Monjur Alahi

8 views

2025-01-04 04:42

1 Answers

Related Questions

The escape velocity form the earth is 11 `kms^(-1)` the esacpe velocity from a planet having twice the radius and the same mean denisty as the earth w

2 Answers 4 Views

The energy spent in sending a body of mass 1 kg surface of the earth infinity is, is escape velocity from the surface of the earth is 12 km/s.

2 Answers 4 Views

The escape velocity of a body projected vertically upwards from the surface of the earth is v.If the body is projected in a direction making an angle

2 Answers 6 Views

The escape velocity of a body from the earth is `V_(e)`. The escape velocity of a planet whose mass and radius are twice those of the earth is

2 Answers 4 Views

The escape velocity from the earth is about 11 km/s. The escape velocity from a planet having twice the radius and the twice mean density as the earth

2 Answers 5 Views

String B has twice the length , twice the diameter twice the tension and twice the density of string A. Then the overtone of B that will be in unison

2 Answers 4 Views

The escape speed of a particle on the surface of the earth is 11.2km/second. A body is projectwith thrice this speed from the surface of the earth. Wh

2 Answers 4 Views

The escape velocity of a body on the surface of the earth is `V_(e)`. What is the escape velocity on a planet whose radius is thrice the radius of the

2 Answers 4 Views

A body is projected from the surface of the earth with thrice the escape velocity `(V_(e))` from the surface of the earth. What will be its velocity,

2 Answers 4 Views

A body is projected vertically upwards from the surface of the earth. If its kinetic energy is equal to half of its minimum value required to escape f

2 Answers 5 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - B
Let `v_(0)` be its velocity in the interplanetary space and v be the velocity of projection `= 2v_(e)`
Then `(1)/(2)mv_(0)^(2)=(1)/(2)mv^(2)-(1)/(2)mv_(e)^(2)`
`=(1)/(2)m(2v_(e))^(2)-(1)/(2)mv_(e)^(2)`
`v_(0)^(2)=4v_(e)^(2)-v_(e)^(2)=3v_(e)^(2)`
`therefore v_(0)=sqrt(3)v_(e)=sqrt(3)sqrt((2GM)/(R ))=sqrt((6GM)/(R ))`