You have landed on Mars, and observe that it takes a stone 1.8 sec to fall 6 m.

Question

You have landed on Mars, and observe that it takes a stone 1.8 sec to fall 6 m.   

(A) What is the acceleration of gravity on Mars?
(B) How much does a 2 kg stone weigh on Mars?
(C) If you could jump to a height of 1.5 m on Earth, how high can you jump on Mars?
(D) If you knew that the mass of Mars was 6.4 x 1023 kg, what would you deduce is its radius?
(E) The Martian moon Deimos has a mass of 3 x 10-9 that of Mars itself.    If Deimos is 2.3 x 107 m away from Mars, how strongly does Mars pull on its small satellite?

Explanation / Answer

Given that

The height from which the stone falled is (h) =6m

The time taken for the stone to fall is (t) =1.8

We know that from the equation of motion

s =ut+(1/2)at2 here u =0

then a =2*6/(1.8)2 =12/3.24 =3.703m/s2

b)

The weight of stone at any place depends upon the acceleration due to gravity . Where as mass remains the same at any place.

W =mg =2*3.703 =7.407N

c)

We know that

W =mgh

from this condition

g1/g2 =h2/h1

9.81/3.703 =h2/1.5 ====>h2 =3.973m

d)

We know that

g =GM/r2 ===>r =Sqrt(GM/g)

e)

F =Gm1m2/r2

Substitute all the values to get the required answer

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