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Q.

A sphere of mass 40 kg is attracted by another sphere of mass 15 kg, when their centers are 20 cm apart, with a force of 0.1 milligram weight. Find the value of G.


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a

6.53×10-11 Nm2kg-2

b

6.53×10-9 Nm2kg-2

c

6.53×10-12  Nm2kg-2

d

6.53×10-12  Nm2kg-2 

answer is A.

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Detailed Solution

The value of G is 6.53×10-11 Nm2kg-2.
By the universal law of gravitation the attractive force between two bodies of masses M and separated by a distance  r is:
     F=GMmr2 ..............(1)
G=Fr2Mm   .................(2)
 Where is the gravitational constant and F is the force of attraction due to the effect of gravitation.
Given:
 Mass of the first object, M=40 kg
Mass of the second object, m=15 kg
Distance separating them, r=0.2 m
Acceleration due to gravity, g=9.8 m/s2 
    =0.1 milligram weight
F=0.1×10-6 kg wt
Therefore,
G=10-7×9.8×0.2×0.240×15
G=6.53×10-11Nm2 kg-2
 
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