Home
Class 11
PHYSICS
If a body is to be projected vertically ...

If a body is to be projected vertically upwards from earth's surface to reach a height of `10R` where `R` is the radius of earth. The velocity required to be si is

A

`sqrt((24)/(11) gr)`

B

`sqrt((22)/(11) gr)`

C

`sqrt((20)/(11) gr)`

D

`sqrt((18)/(11) gr)`

Text Solution

Verified by Experts

The correct Answer is:
C
From law of conservation of energy, we have
`-(GM m)/(R ) + (1)/(2) m upsilon^(2) = - (GM m)/((10 R + R)) + 0 = - (GM m)/(11R)`
or `(1)/(2) upsilon^(2) = (GM)/(R ) - (GM)/(11R) = (10)/(11)(GM)/(R )`
or `upsilon^(2) = (20)/(11) (GM)/(R ) = (20)/(11)g R` or `upsilon = sqrt((20g R)/(11))`
Promotional Banner

Similar Questions

Explore conceptually related problems

A body is to be projected vertically upwards from earth's surface to reach a height of 9R , where R is the radius of earth. What is the velocity required to do so? Given g=10ms^(-2) and radius of earth =6.4xx10^(6)m .

The initial velocity v_(i) required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity v_(e ) such that v_(i)= sqrt((x)/(y)) xx v_(e ) . The value of x will be __________ .

Calculate the velocity with which a body must be thrown vertically upward from the surface of the earth so that it may reach a height of 10R , where R is the radius of the earth and is equal to 6.4 xx 10^(6)m. (Given: Mass of the earth = 6 xx 10^(24) kg , gravitational constant G = 6.7 xx 10^(-11) N m^(2) kg^(-2) )

A body is projected vertically upwards from the earth's surface. The body reaches a height equal to one half of radius of earth. Calculate the initial speed with which the body was projected initially. Radius of earth = 6,400 km Mass of earth = 6 xx 10^(24) kg

A body is projected vertically upward from the surface of the earth, then the velocity-time graph is:-

A body is projected vertically upwards from the surface of earth with a velocity equal to half the escape velocity. If R be the radius of earth, maximum height attained by the body from the surface of earth is ( R)/(n) . Find the value of n.

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

A particle is throws vertically upwards from the surface of earth and it reaches to a maximum height equal to the radius of earth. The radio of the velocity of projection to the escape velocity on the surface of earth is

Show that if a body be projected vertically upward from the surface of the earth so as to reach a height nR above the surface (i) the increase in its potential energy is ((n)/(n + 1)) mgR , (ii) the velocity with it must be projected is sqrt((2ngR)/(n + 1)) , where r is the radius of the earth and m the mass of body.