Question

a planet has mass and radious 1/3 of those of earth.calculat it's weight on planet​

Answer 1

Explanation:

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Answer 2

Let us consider the mass of planet is M.

The radius of earth is R.

Hence, the gravitational acceleration of the earth is calculated as -

g=G\frac{M}{R^2}g=G

R

2

M

Here, G is the universal gravitational force constant.

The value of g\ =\ 9.8\ m/s^2g = 9.8 m/s

2

.

As per the question, the mass of other planet M' = \frac{1}{3}M

3

1

M

The radius of the planet R' = \frac{1}{3}R

3

1

R

Hence, the acceleration due to gravity on this planet will be -

g'=G\frac{M/3}{(R/3)^2}g

′

=G

(R/3)

2

M/3

=G\frac{M}{3}\times \frac{9}{R^2}=G

3

M

×

R

2

9

=\ 3G\frac{M}{R^2}= 3G

R

2

M

[2]

From above, we see that the acceleration due to gravity on this planet is three times the acceleration due to gravity on earth.

Hence, g ' = 3g.

Again we are asked to calculate the weight of a 5 kg object on this planet.

The mass of a body is always constant for non relativistic motion. So, the mass of the object on this planet will be the same i.e 5 kg.

The weight of a body is equal to the product of mass with aceleration due to gravity.

Hence, the weight of the object on this new planet will be-

W = mg'

= 5×3g N.

= 5×3×9.8 N

= 147 N. [ ans]