Assume that the acceleration due to gravity on surface of the moon is $0.2$ times the acceleration due to gravity on the surface of earth. If $R_{e}$ is the maximum range of a projectile on the earth's surface, what is the maximum range on the surface of the moon for the same velocity of projection

0.2 R_{e}

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2 R_{e}

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0.5 R_{e}

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5 R_{e}

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Solution

The correct option is D $5 R_{e}$
The maximum range of a projectile motion is given by: $R_{m a x} = \frac{U^{2}}{g}$
$\Rightarrow R \propto \frac{1}{g}$
$\Rightarrow \frac{R_{m}}{R_{e}} = \frac{g_{e}}{g_{m}} = \frac{g_{e}}{0.2 g_{e}} = \frac{1}{0.2} = 5$
$∴ R_{m} = 5 R_{e}$

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Assume that the acceleration due to gravity on surface of the moon is 0.2 times the acceleration due to gravity on the surface of earth. If Re is the maximum range of a projectile on the earth's surface, what is the maximum range on the surface of the moon for the same velocity of projection

The correct option is D 5ReThe maximum range of a projectile motion is given by: Rmax=U2g⇒R∝1g⇒RmRe=gegm=ge0.2ge=10.2=5∴Rm=5Re

Assume that the acceleration due to gravity on surface of the moon is $0.2$ times the acceleration due to gravity on the surface of earth. If $R_{e}$ is the maximum range of a projectile on the earth's surface, what is the maximum range on the surface of the moon for the same velocity of projection

The correct option is D $5 R_{e}$
The maximum range of a projectile motion is given by: $R_{m a x} = \frac{U^{2}}{g}$
$\Rightarrow R \propto \frac{1}{g}$
$\Rightarrow \frac{R_{m}}{R_{e}} = \frac{g_{e}}{g_{m}} = \frac{g_{e}}{0.2 g_{e}} = \frac{1}{0.2} = 5$
$∴ R_{m} = 5 R_{e}$