Question

On a planet whose size is the same and mass 4 times as that of the earth, find the energy needed to left a 2kg mass vertically upward through 2m distance in joule. take g= 10m/sec²​

Answer 1

Explanation:

ANSWER

On the planet,  g′=R2G×4M

On the earth,   g=R2GM

∴gg′=4

⇒g′=4g=40m/s2

Energy needed to lift 2 kg mass through 2 m distance,

E=mg′h

=2×40×2

=160 joules.

Answer 2

${\mathfrak{\underline{\purple{\:\:\: Given:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\textsf{On a planet (whose size is the same and mass 4 times as that of the earth), the energy needed to lift a 2 kg mass vertically upwards through 2m}$

${\mathfrak{\underline{\purple{\:\:\:To \:Find:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\textsf{Distance (in joule)}$

${\mathfrak{\underline{\purple{\:\:\: Solution:-\:\:\:}}}}$

☯ On the planet

$\:\:\:\:\bullet\:\:\:\sf{g' = \dfrac{G\times 4M}{R^2}}$

☯ On the earth

$\:\:\:\:\bullet\:\:\:\sf{g = \dfrac{GM}{R^2}}$

$\dashrightarrow\:\: \sf{ \dfrac{g'}{g} = 4}$

$\dashrightarrow\:\: \sf{g' = 4g }$

$\dashrightarrow\:\: \sf{g' = 40m/s^2 }$

$\bigstar\:\textsf{Energy needed to lift 2 kg mass through 2 m distance,}$

$\dashrightarrow\:\: \sf{E=mg'h}$

$\dashrightarrow\:\: \sf{2\times 40 \times 2}$

$\dashrightarrow\:\: {\boxed{\bf{160\:Joules}}}$