NTSE Stage 2 SAT 2017 Question Paper

Question : 34 of 100

Marks: +1, -0

An object falls a distance H in 50 s when dropped on the surface of the earth. How long would it take for the same object to fall through the same distance on the surface of a planet whose mass and radius are twice that of the earth ? (Neglect air resistance.)

35.4 g
50.0 s
70.7 s
100.0 s

Validate

Solution:

\g=10 \m / \;\s^2 \on \earth

\;\;=\GM/\R^2

\g'=\GM'/\R'^2={2×\GM}/{4\R^2}

\;\;\;\=\g/2=5 \m\;/\s^2

\h=1/2\gt^2=1/2\g'\t'^2

⇒

\t'=√{{10×50×50}/5}

\;\;\;\;\;\;=√2×50

\;\;\;\;\;\;\=70.7 \s

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