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Calculate the velocity with which a body...

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)`)

Text Solution

Verified by Experts

The correct Answer is:
`1.07xx10^(4)ms^(-1)`
Conservation of energy gives
`1/2mv^(2)-(GMm)/R=0-(GMm)/((R+10R))`
`v=sqrt((20/11(Gm)/R)=1.07xx10^(4)ms^(-1)`
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Calculate the velocity with which a body must be thrown vertically from the surface of the earth so that it may reach a height of 10R , where R is the radus of the earth and is equal to 6.4xx10^(8)m . (earth's mass =6xx10^(24)kg , gravitational constant G=6.7xx10^(-11)Nm^(2)kg^(-2))

With what velocity must a body be thrown upward form the surface of the earth so that it reaches a height of 10 R_(e) ? earth's mass M_(e) = 6 xx 10^(24) kg , radius R_(e) = 6.4 xx 10^(6) m and G = 6.67 xx 10^(-11) N-m^(2)//kg^(2) .

Knowledge Check

  • 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)`

  • 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 .

    A
    `1.073xx10^(4) ms^(-1)`
    B
    `1.73xx10^(4) ms^(-1)`
    C
    `10.73xx10^(4) ms^(-1)`
    D
    `17.3xx10^(4) ms^(-1)`

  • Determine the gravitational potential on the surface of earth, given that radius of the earth is 6.4 xx 10^(6) m : its mean density is 5.5 xx 10^(3)kg m^(-3) , G = 6.67 xx 10^(-11) Nm^(2) kg^(-2) .

    A
    `-6.297 xx 10^(7) J kg^(-1)`
    B
    `3.11 xx 10^(11) J kg^(-1)`
    C
    `4 xx 10^(8) J kg^(-1)`
    D
    `-2 xx 10^(9) J kg^(-1)`

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    With what velocity must a body be projected vertically upwards from the surface of the earth in orer that it may never return to the earth ? ( G = 6.66 10 ^(-11) SI units , mean density of the earth = 5.525 xx 10^(3) kg m^(-3) , radius of the earth = 6.38 xx 10 ^(6) m.)

    A body is projected vertically upwards from the surface of the Earth so as to reach a height equal to the radius of the Earth. Neglecting resistance due to it, calculate the initial speed which should be imparted to the body. Mass of Earth = 5.98 xx 10^(24) kg , Radius of Earth = 6400 km , G = 6.67 xx 10^(-11) Nm^(2) kg^(-2) .

    Calculate the gravitational potential energy of a body of mass 30 kg , at a height of 4 R from the surface of Earth, where R (= 6.4 xx 10^(6) m) is the radius of the Earth. Mass of the Earth = 6.0 xx 10^(24) kg, G = 6.67 xx 10^(-11) Nm^(2) kg^(-2) .

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