Question

EXAMPLE 3.11: A man weighs 600 N on the earth. If acceleration due to gravity g on the
10 m s -2, what is his mass?
On the moon, weight of the man is found to be 100 N. What is the value of g on the moc​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:g\:on\:moon=\frac{5}{3}\:m/s^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Weight \: of \: man \: on \: earth = 600 \: N\\ \\ \tt: \implies Acceleration \: due \:to \: gravity(g) = 10 { \: m/s}^{2} \\ \\ \tt: \implies Weight \: of \: man \: on \: moon = 100 \: N \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Value \: of \: g \: on \: moon =?$

• According to given question :

$\bold{For \: weight \: of \: man \: on \: earth} \\ \tt: \implies Weight \: of \: man \: on \: earth = mg \\ \\ \tt: \implies 600 = m \times 10 \\ \\ \tt: \implies m = \frac{600}{10} \\ \\ \green{\tt: \implies m = 60 \: kg} \\ \\ \bold{For \: weight \: of \: man \: on \: moon} \\ \\ \tt \circ \: Mass \: of \: man \: is \: constant \\ \tt: \implies Weight \: of \: man \: of \: moon = mg_{1} \\ \\ \tt: \implies 100 = 60 \times g_{1} \\ \\ \tt: \implies g_{1} = \frac{100}{60} \\ \\ \tt: \implies g_{1} = \frac{10}{6} \\ \\ \green{\tt: \implies g_{1} = \frac{5}{3} \: {m/s}^{2}}$

Answer 2

Question  -

A man weighs 600 N on the earth.

If acceleration due to gravity g on the

10 m s -2, what is his mass?

On the moon, weight of the man is found to be 100 N.

What is the value of g on the moc​n?

Solution -

In the above question, the following information is given -

A man weighs 600 N on the earth.

The, acceleration due to gravity g on the  surface Of The Earth is $10 \: m  . {s}^{-2}$

We know that ,

According to The Newton's Laws Of Motion,

$\sf{ \color{\teal} { F = m \times a }} \\ \\ \sf{\leadsto { Where \: - }} \\ \\ \tt{ F \: is \: the \: Force } \\ \\ \tt{ m \: is \: the \: mass \: of \: the \: object } \\ \\ \sf{ a \: is \: the \: acceleration }$

Now. Here -

Substuting The Required Values -

Weight = m * g

=> 600 = m * 10

=> m = 60 kg.

Hence, the required mass of the man on earth is 60 kg.

Now,

On the moon, weight of the man is found to be 100 N .

Let the acceleration due to gravity on the moon  be k

Using the similar relation mentioned above -

100 = 60 * k

=> k = [ 100 / 60 ] = [ 5 / 3 ] m . s^( -2 ) .

So, the value of acceleration due to gravity on the moon is [ 5 / 3 ] m . s^( -2 )  .

Answer

The value of acceleration due to gravity on the moon is [ 5 / 3 ] m . s^( -2 )  .