A body of mass m falls from a height R above surface of earth, where R &nb

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7.Gravitation

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A body of mass $m$ falls from a height $R$ above the surface of the earth, where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$ )

$gR$

$\sqrt {gR}$

$\sqrt {g/R}$

$g/R$

Solution

According to conservation of energy

$\frac{-\mathrm{GMm}}{2 \mathrm{R}}+0=-\frac{\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{mv}^{2}$

$\Rightarrow \frac{\mathrm{GMm}}{2 \mathrm{R}}=\frac{1}{2} \mathrm{mv}^{2} \Rightarrow \mathrm{v}^{2}=\frac{\mathrm{GM}}{\mathrm{R}}=\frac{\mathrm{GM}}{\mathrm{R}^{2}} \times \mathrm{R}$

$\Rightarrow \quad v=\sqrt{g R}$

Standard 11

Physics

Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth $= R_E$ )?

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The escape velocity for a body projected vertically upwards from the surface of earth is $11\, km/s$. If the body is projected at an angle of $45^o$ with the vertical, the escape velocity will be ……….. $km/s$

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Which of the following statements are true about acceleration due to gravity?

$(a)\,\,'g'$ decreases in moving away from the centre if $r > R$

$(b)\,\,'g'$ decreases in moving away from the centre if $r < R$

$(c)\,\,'g'$ is zero at the centre of earth

$(d)\,\,'g'$ decreases if earth stops rotating on its axis

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On a hypothetical planet satellite can only revolve in quantized energy level i.e. magnitude of energy of a satellite is integer multiple of a fixed energy. If two successive orbit have radius $R$ and $\frac{3R}{2}$ what could be maximum radius of satellite

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A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V.$ Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

normal

A body of mass $m$ falls from a height $R$ above the surface of the earth, where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$ )

Solution

Similar Questions

Which graph correctly presents the variation of acceleration due to gravity with the distance from the centre of the earth (radius of the earth $= R_E$ )?

The escape velocity for a body projected vertically upwards from the surface of earth is $11\, km/s$. If the body is projected at an angle of $45^o$ with the vertical, the escape velocity will be ……….. $km/s$

On a hypothetical planet satellite can only revolve in quantized energy level i.e. magnitude of energy of a satellite is integer multiple of a fixed energy. If two successive orbit have radius $R$ and $\frac{3R}{2}$ what could be maximum radius of satellite

A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V.$ Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

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