A body, when weighed on surface of earth and on moon, has weights $30 N$ and $6 N$ respectively. If acceleration due to gravity on the surface of the earth is $10 m s^{- 2}$ , what will be the acceleration due to gravity on the surface of moon.

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Solution

Step 1:Given
$g_{e} = 10 m s^{- 2} w h e r e, g_{e} \to a c c e l e r a t i o n d u e t o g r a v i t y o n e a r t h A c c e l e r a t i o n d u e t o g r a v i t y o n m o o n, g_{m} = ? W e i g h t o f t h e b o d y o n e a r t h, W_{e} = 30 N W e i g h t o f t h e b o d y o n m o o n, W_{m} = 6 N$
Step 2: Writing the expressions for weight on earth and moon in terms of mass and acceleration due to gravity.
$L e t u s a s s u m e, m a s s o f t h e b o d y \to M S o, W_{e} = M \times g_{e} W_{m} = M \times g_{m}$
Step 3: Comparing the weights to find out the acceleration due to gravity on moon.
$\frac{W_{e}}{W_{m}} = \frac{M \times g_{e}}{M \times g_{m}} = \frac{g_{e}}{g_{m}}$
Step 4: Substituting the given values to find the value of $g_{m}$ .
$\frac{W_{e}}{W_{m}} = \frac{g_{e}}{g_{m}} \frac{30}{6} = \frac{10}{g_{m}} g_{m} = \frac{6 \times 10}{30} = 2 m s^{- 2}$
Hence, the acceleration due to gravity on Moon comes out to be $2 m s^{- 2}$ .

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A body, when weighed on surface of earth and on moon, has weights 30N and 6N respectively. If acceleration due to gravity on the surface of the earth is 10ms-2, what will be the acceleration due to gravity on the surface of moon.

A body, when weighed on surface of earth and on moon, has weights $30 N$ and $6 N$ respectively. If acceleration due to gravity on the surface of the earth is $10 m s^{- 2}$ , what will be the acceleration due to gravity on the surface of moon.