Page 42 - Force 10

Conditions:

3) When the distance between their centre and their masses both changed.

a) If the mass of one object is doubled, another object is tripled and distance between their centre is halved.
st
Ans: Case I let the mass of 1 object be m kg, m 1 m 2
1
nd
the mass of 2 object be m kg,
2
& distance between their centres be d m.
× 2 … (i)
1
According to the Newton’s law of gravitation: F = G 2 d
1

st
Case II let the mass of 1 object ( m ) = 2 m kg, A B
1
1
nd
the mass of 2 object (m ) = 3 m kg,
2
2
& distance between their centres be d/2 m. 2 m 1 3 m 2
× 2 … (ii)
1
According to the Newton’s law of gravitation: F = G 2
2
2 × 3 2
1
= G d/2
( ) 2
2 A B
× 2
1
= 6 × 4 × G
2

= 24 F 1

∴ F = 24 F 1
2

Hence, the new gravitational force is increased by 24 times than the initial force.